The question was if it was possible or not.

 

As the percentage of it occurring approaches abs. 0, n will rise to infinity.

 

In order for it to actually reach the hypothetical infinity, the percentage would have to be abs. 0, therefore 0 percent chance of it occurring.

 

 

 

I am sorry, but you cannot divide by infinity, because infinity is not a number, it is a concept.

 

 

 

 

 

i'd say it's possible, but near impossible.

I just proved it's impossible! 0% chance, as in it cannot happen

 

Your whole case seems to rest on your belief which you've "simplified" as "any number divided by infinity = 0. "

Which, you pulled out of your ass- It is not factually based, at all. I don't know where you got that from.

You're going to have to provide actual evidence that it is a 0% chance. Provide, for example, the number of times in which the coin is flipped where, from there on out it can reach heads no longer. I would be very interested, as that makes no sense at all.

Read Zappa's post.

 

 

 

 

Note: You cannot actually divide by infinity, I added this just for simplicity. Instead of dividing by infinity, you would take the limit of 1/x as x goes to infinity. For those who do not yet know what limits are, basically if x becomes really really really really big, what number does 1/x tend towards?

 

 

 

 

I'm just going to assume you both missed that part of the post...I did indeed prove that if you flipped a coin an infinite amount of times, there is a 0% chance that you would get heads every time.

 

I'll try to explain again, but first, you have to understand what flipping a coin an infinite amount of times means. Infinity is not a number, so when you do something an "infinite amount of times", it means you cannot put a number on the amount of times you flipped that coin, the amount of times it is flipped is never ending.

 

Obviously your idea of "at some point in time it will have to be tails" is ridiculous if you are trying to come up with some type of actual proof. But once again, I will state the logical outcome of flipping a coin an infinite amount of times, and try to explain it better.

 

If you flip a coin, the chances of it landing on heads x times in a row is 1/2^x for x greater than 0. If we are going to perform this task an infinite amount of times, this means we have to take the limit as x approaches infinity of 1/2^x. The limit of this is 0, if you need a proof on limits, go google it.

 

Now you might be saying, "but wait!!, just because the limit is zero doesn't mean it actually reaches 0!!", yes, that is true, but in reality you also never reach infinity, because there is always a number which is bigger than whatever one you are on. 

 

The point is, if you COULD flip a coin for an infinite amount of trials, the probability of having heads for every one of that infinite set of trials would be exactly zero. What you seem to be wanting to know is if there is some specific point where the probability becomes zero, and that point is one infinitely far away, a point which we can never reach in reality.

 

So to clarify things further, doing an infinite amount of trials is just taking a limit, because you can't actually do an infinite amount of trials. The only way to deal with infinities is to use limits, to see what number the function approaches as you approach infinity.

 

And to make things more interesting for you, for x E N ( x is an element of the Natural set of Numbers), for every x, there is a non-zero probability that you will flip heads every time, where x is the number of times you flip the coin. BUT, IF YOU FLIP A COIN AN INFINITE AMOUNT OF TIMES, THE PROBABILITY BECOMES ZERO

 

I hope that will convince you that there is indeed a 0 probability, but then again, I don't think you understand your question yet.

 

I am sorry, but you cannot divide by infinity, because infinity is not a number, it is a concept.

 

 

 

 

 

i'd say it's possible, but near impossible.

I just proved it's impossible! 0% chance, as in it cannot happen

 

Your whole case seems to rest on your belief which you've "simplified" as "any number divided by infinity = 0. "

Which, you pulled out of your ass- It is not factually based, at all. I don't know where you got that from.

You're going to have to provide actual evidence that it is a 0% chance. Provide, for example, the number of times in which the coin is flipped where, from there on out it can reach heads no longer. I would be very interested, as that makes no sense at all.

Read Zappa's post.

 

 

 

 

Note: You cannot actually divide by infinity, I added this just for simplicity. Instead of dividing by infinity, you would take the limit of 1/x as x goes to infinity. For those who do not yet know what limits are, basically if x becomes really really really really big, what number does 1/x tend towards?

 

 

 

 

I'm just going to assume you both missed that part of the post...I did indeed prove that if you flipped a coin an infinite amount of times, there is a 0% chance that you would get heads every time.

 

I'll try to explain again, but first, you have to understand what flipping a coin an infinite amount of times means. Infinity is not a number, so when you do something an "infinite amount of times", it means you cannot put a number on the amount of times you flipped that coin, the amount of times it is flipped is never ending.

 

Obviously your idea of "at some point in time it will have to be tails" is ridiculous if you are trying to come up with some type of actual proof. But once again, I will state the logical outcome of flipping a coin an infinite amount of times, and try to explain it better.

 

If you flip a coin, the chances of it landing on heads x times in a row is 1/2^x for x greater than 0. If we are going to perform this task an infinite amount of times, this means we have to take the limit as x approaches infinity of 1/2^x. The limit of this is 0, if you need a proof on limits, go google it.

 

Now you might be saying, "but wait!!, just because the limit is zero doesn't mean it actually reaches 0!!", yes, that is true, but in reality you also never reach infinity, because there is always a number which is bigger than whatever one you are on. 

 

The point is, if you COULD flip a coin for an infinite amount of trials, the probability of having heads for every one of that infinite set of trials would be exactly zero. What you seem to be wanting to know is if there is some specific point where the probability becomes zero, and that point is one infinitely far away, a point which we can never reach in reality.

 

So to clarify things further, doing an infinite amount of trials is just taking a limit, because you can't actually do an infinite amount of trials. The only way to deal with infinities is to use limits, to see what number the function approaches as you approach infinity.

 

And to make things more interesting for you, for x E N ( x is an element of the Natural set of Numbers), for every x, there is a non-zero probability that you will flip heads every time, where x is the number of times you flip the coin. BUT, IF YOU FLIP A COIN AN INFINITE AMOUNT OF TIMES, THE PROBABILITY BECOMES ZERO

 

I hope that will convince you that there is indeed a 0 probability, but then again, I don't think you understand your question yet.

 

"The limit of this is 0, if you need a proof on limits, go google it."

I did, first two sources say you're wrong.

http://www.mathsisfun.com/calculus/limits-infinity.html

https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/liminfdirectory/LimitInfinity.html

You are trying to say the limit to infinity is 0, it is not, and CANNOT be calculated because infinity is not a number.

 

I am sorry, but you cannot divide by infinity, because infinity is not a number, it is a concept.

 

 

 

 

 

i'd say it's possible, but near impossible.

I just proved it's impossible! 0% chance, as in it cannot happen

 

Your whole case seems to rest on your belief which you've "simplified" as "any number divided by infinity = 0. "

Which, you pulled out of your ass- It is not factually based, at all. I don't know where you got that from.

You're going to have to provide actual evidence that it is a 0% chance. Provide, for example, the number of times in which the coin is flipped where, from there on out it can reach heads no longer. I would be very interested, as that makes no sense at all.

Read Zappa's post.

 

 

 

 

Note: You cannot actually divide by infinity, I added this just for simplicity. Instead of dividing by infinity, you would take the limit of 1/x as x goes to infinity. For those who do not yet know what limits are, basically if x becomes really really really really big, what number does 1/x tend towards?

 

 

 

 

I'm just going to assume you both missed that part of the post...I did indeed prove that if you flipped a coin an infinite amount of times, there is a 0% chance that you would get heads every time.

 

I'll try to explain again, but first, you have to understand what flipping a coin an infinite amount of times means. Infinity is not a number, so when you do something an "infinite amount of times", it means you cannot put a number on the amount of times you flipped that coin, the amount of times it is flipped is never ending.

 

Obviously your idea of "at some point in time it will have to be tails" is ridiculous if you are trying to come up with some type of actual proof. But once again, I will state the logical outcome of flipping a coin an infinite amount of times, and try to explain it better.

 

If you flip a coin, the chances of it landing on heads x times in a row is 1/2^x for x greater than 0. If we are going to perform this task an infinite amount of times, this means we have to take the limit as x approaches infinity of 1/2^x. The limit of this is 0, if you need a proof on limits, go google it.

 

Now you might be saying, "but wait!!, just because the limit is zero doesn't mean it actually reaches 0!!", yes, that is true, but in reality you also never reach infinity, because there is always a number which is bigger than whatever one you are on. 

 

The point is, if you COULD flip a coin for an infinite amount of trials, the probability of having heads for every one of that infinite set of trials would be exactly zero. What you seem to be wanting to know is if there is some specific point where the probability becomes zero, and that point is one infinitely far away, a point which we can never reach in reality.

 

So to clarify things further, doing an infinite amount of trials is just taking a limit, because you can't actually do an infinite amount of trials. The only way to deal with infinities is to use limits, to see what number the function approaches as you approach infinity.

 

And to make things more interesting for you, for x E N ( x is an element of the Natural set of Numbers), for every x, there is a non-zero probability that you will flip heads every time, where x is the number of times you flip the coin. BUT, IF YOU FLIP A COIN AN INFINITE AMOUNT OF TIMES, THE PROBABILITY BECOMES ZERO

 

I hope that will convince you that there is indeed a 0 probability, but then again, I don't think you understand your question yet.

 

The math behind my answer haha.

 

 

I am sorry, but you cannot divide by infinity, because infinity is not a number, it is a concept.

 

 

 

 

 

i'd say it's possible, but near impossible.

I just proved it's impossible! 0% chance, as in it cannot happen

 

Your whole case seems to rest on your belief which you've "simplified" as "any number divided by infinity = 0. "

Which, you pulled out of your ass- It is not factually based, at all. I don't know where you got that from.

You're going to have to provide actual evidence that it is a 0% chance. Provide, for example, the number of times in which the coin is flipped where, from there on out it can reach heads no longer. I would be very interested, as that makes no sense at all.

Read Zappa's post.

 

 

 

 

Note: You cannot actually divide by infinity, I added this just for simplicity. Instead of dividing by infinity, you would take the limit of 1/x as x goes to infinity. For those who do not yet know what limits are, basically if x becomes really really really really big, what number does 1/x tend towards?

 

 

 

 

I'm just going to assume you both missed that part of the post...I did indeed prove that if you flipped a coin an infinite amount of times, there is a 0% chance that you would get heads every time.

 

I'll try to explain again, but first, you have to understand what flipping a coin an infinite amount of times means. Infinity is not a number, so when you do something an "infinite amount of times", it means you cannot put a number on the amount of times you flipped that coin, the amount of times it is flipped is never ending.

 

Obviously your idea of "at some point in time it will have to be tails" is ridiculous if you are trying to come up with some type of actual proof. But once again, I will state the logical outcome of flipping a coin an infinite amount of times, and try to explain it better.

 

If you flip a coin, the chances of it landing on heads x times in a row is 1/2^x for x greater than 0. If we are going to perform this task an infinite amount of times, this means we have to take the limit as x approaches infinity of 1/2^x. The limit of this is 0, if you need a proof on limits, go google it.

 

Now you might be saying, "but wait!!, just because the limit is zero doesn't mean it actually reaches 0!!", yes, that is true, but in reality you also never reach infinity, because there is always a number which is bigger than whatever one you are on. 

 

The point is, if you COULD flip a coin for an infinite amount of trials, the probability of having heads for every one of that infinite set of trials would be exactly zero. What you seem to be wanting to know is if there is some specific point where the probability becomes zero, and that point is one infinitely far away, a point which we can never reach in reality.

 

So to clarify things further, doing an infinite amount of trials is just taking a limit, because you can't actually do an infinite amount of trials. The only way to deal with infinities is to use limits, to see what number the function approaches as you approach infinity.

 

And to make things more interesting for you, for x E N ( x is an element of the Natural set of Numbers), for every x, there is a non-zero probability that you will flip heads every time, where x is the number of times you flip the coin. BUT, IF YOU FLIP A COIN AN INFINITE AMOUNT OF TIMES, THE PROBABILITY BECOMES ZERO

 

I hope that will convince you that there is indeed a 0 probability, but then again, I don't think you understand your question yet.

 

"The limit of this is 0, if you need a proof on limits, go google it."

I did, first two sources say you're wrong.

http://www.mathsisfun.com/calculus/limits-infinity.html

https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/liminfdirectory/LimitInfinity.html

You are trying to say the limit to infinity is 0, it is not, and CANNOT be calculated because infinity is not a number.

 

 

But We Can Approach It!

So instead of trying to work it out for infinity (because we can't get a sensible answer), let's try larger and larger values of x:

x 1/x 1 1.00000 2 0.50000 4 0.25000 10 0.10000 100 0.01000 1,000 0.00100 10,000 0.00010    

Now we can see that as x gets larger, 1/x tends towards 0

Literally first link, first page.

 

 

I am sorry, but you cannot divide by infinity, because infinity is not a number, it is a concept.

 

 

 

 

 

i'd say it's possible, but near impossible.

I just proved it's impossible! 0% chance, as in it cannot happen

 

Your whole case seems to rest on your belief which you've "simplified" as "any number divided by infinity = 0. "

Which, you pulled out of your ass- It is not factually based, at all. I don't know where you got that from.

You're going to have to provide actual evidence that it is a 0% chance. Provide, for example, the number of times in which the coin is flipped where, from there on out it can reach heads no longer. I would be very interested, as that makes no sense at all.

Read Zappa's post.

 

 

 

 

Note: You cannot actually divide by infinity, I added this just for simplicity. Instead of dividing by infinity, you would take the limit of 1/x as x goes to infinity. For those who do not yet know what limits are, basically if x becomes really really really really big, what number does 1/x tend towards?

 

 

 

 

I'm just going to assume you both missed that part of the post...I did indeed prove that if you flipped a coin an infinite amount of times, there is a 0% chance that you would get heads every time.

 

I'll try to explain again, but first, you have to understand what flipping a coin an infinite amount of times means. Infinity is not a number, so when you do something an "infinite amount of times", it means you cannot put a number on the amount of times you flipped that coin, the amount of times it is flipped is never ending.

 

Obviously your idea of "at some point in time it will have to be tails" is ridiculous if you are trying to come up with some type of actual proof. But once again, I will state the logical outcome of flipping a coin an infinite amount of times, and try to explain it better.

 

If you flip a coin, the chances of it landing on heads x times in a row is 1/2^x for x greater than 0. If we are going to perform this task an infinite amount of times, this means we have to take the limit as x approaches infinity of 1/2^x. The limit of this is 0, if you need a proof on limits, go google it.

 

Now you might be saying, "but wait!!, just because the limit is zero doesn't mean it actually reaches 0!!", yes, that is true, but in reality you also never reach infinity, because there is always a number which is bigger than whatever one you are on. 

 

The point is, if you COULD flip a coin for an infinite amount of trials, the probability of having heads for every one of that infinite set of trials would be exactly zero. What you seem to be wanting to know is if there is some specific point where the probability becomes zero, and that point is one infinitely far away, a point which we can never reach in reality.

 

So to clarify things further, doing an infinite amount of trials is just taking a limit, because you can't actually do an infinite amount of trials. The only way to deal with infinities is to use limits, to see what number the function approaches as you approach infinity.

 

And to make things more interesting for you, for x E N ( x is an element of the Natural set of Numbers), for every x, there is a non-zero probability that you will flip heads every time, where x is the number of times you flip the coin. BUT, IF YOU FLIP A COIN AN INFINITE AMOUNT OF TIMES, THE PROBABILITY BECOMES ZERO

 

I hope that will convince you that there is indeed a 0 probability, but then again, I don't think you understand your question yet.

 

"The limit of this is 0, if you need a proof on limits, go google it."

I did, first two sources say you're wrong.

http://www.mathsisfun.com/calculus/limits-infinity.html

https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/liminfdirectory/LimitInfinity.html

You are trying to say the limit to infinity is 0, it is not, and CANNOT be calculated because infinity is not a number.

 

 

To bad you didn't actually read the links you posted, or you might have learned something...Once you finish highschool math, you will learn that you can in fact take limits to infinity. All of calculus is based around this concept. 

 

And in case you still have doubts, you can just use a calculator http://www.wolframalpha.com/input/?i=lim+x-%3Einfinity+1%2Fx.

 

The only real issue you could have with this is that a limit is the number you are approaching, not one you actually ever reach. But it is the same concept as you never actually reaching infinity, because there is no sign that says "Here, this is infinity, you've gone far enough".

 

But when you say you flip a coin an infinite amount of times, then you are just hypothetically saying "what if we could reach infinity", well then, we would also reach 0 probability.

 

 

 

I am sorry, but you cannot divide by infinity, because infinity is not a number, it is a concept.

 

 

 

 

 

i'd say it's possible, but near impossible.

I just proved it's impossible! 0% chance, as in it cannot happen

 

Your whole case seems to rest on your belief which you've "simplified" as "any number divided by infinity = 0. "

Which, you pulled out of your ass- It is not factually based, at all. I don't know where you got that from.

You're going to have to provide actual evidence that it is a 0% chance. Provide, for example, the number of times in which the coin is flipped where, from there on out it can reach heads no longer. I would be very interested, as that makes no sense at all.

Read Zappa's post.

 

 

 

 

Note: You cannot actually divide by infinity, I added this just for simplicity. Instead of dividing by infinity, you would take the limit of 1/x as x goes to infinity. For those who do not yet know what limits are, basically if x becomes really really really really big, what number does 1/x tend towards?

 

 

 

 

I'm just going to assume you both missed that part of the post...I did indeed prove that if you flipped a coin an infinite amount of times, there is a 0% chance that you would get heads every time.

 

I'll try to explain again, but first, you have to understand what flipping a coin an infinite amount of times means. Infinity is not a number, so when you do something an "infinite amount of times", it means you cannot put a number on the amount of times you flipped that coin, the amount of times it is flipped is never ending.

 

Obviously your idea of "at some point in time it will have to be tails" is ridiculous if you are trying to come up with some type of actual proof. But once again, I will state the logical outcome of flipping a coin an infinite amount of times, and try to explain it better.

 

If you flip a coin, the chances of it landing on heads x times in a row is 1/2^x for x greater than 0. If we are going to perform this task an infinite amount of times, this means we have to take the limit as x approaches infinity of 1/2^x. The limit of this is 0, if you need a proof on limits, go google it.

 

Now you might be saying, "but wait!!, just because the limit is zero doesn't mean it actually reaches 0!!", yes, that is true, but in reality you also never reach infinity, because there is always a number which is bigger than whatever one you are on. 

 

The point is, if you COULD flip a coin for an infinite amount of trials, the probability of having heads for every one of that infinite set of trials would be exactly zero. What you seem to be wanting to know is if there is some specific point where the probability becomes zero, and that point is one infinitely far away, a point which we can never reach in reality.

 

So to clarify things further, doing an infinite amount of trials is just taking a limit, because you can't actually do an infinite amount of trials. The only way to deal with infinities is to use limits, to see what number the function approaches as you approach infinity.

 

And to make things more interesting for you, for x E N ( x is an element of the Natural set of Numbers), for every x, there is a non-zero probability that you will flip heads every time, where x is the number of times you flip the coin. BUT, IF YOU FLIP A COIN AN INFINITE AMOUNT OF TIMES, THE PROBABILITY BECOMES ZERO

 

I hope that will convince you that there is indeed a 0 probability, but then again, I don't think you understand your question yet.

 

"The limit of this is 0, if you need a proof on limits, go google it."

I did, first two sources say you're wrong.

http://www.mathsisfun.com/calculus/limits-infinity.html

https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/liminfdirectory/LimitInfinity.html

You are trying to say the limit to infinity is 0, it is not, and CANNOT be calculated because infinity is not a number.

 

 

But We Can Approach It!

So instead of trying to work it out for infinity (because we can't get a sensible answer), let's try larger and larger values of x:

x 1/x 1 1.00000 2 0.50000 4 0.25000 10 0.10000 100 0.01000 1,000 0.00100 10,000 0.00010    

Now we can see that as x gets larger, 1/x tends towards 0

Literally first link, first page.

 

yes... I agree with that? are you on my side or against me? That is my stance... that it gets incredibly small, but never actually reaches zero.

 

 

 

I am sorry, but you cannot divide by infinity, because infinity is not a number, it is a concept.

 

 

 

 

 

i'd say it's possible, but near impossible.

I just proved it's impossible! 0% chance, as in it cannot happen

 

Your whole case seems to rest on your belief which you've "simplified" as "any number divided by infinity = 0. "

Which, you pulled out of your ass- It is not factually based, at all. I don't know where you got that from.

You're going to have to provide actual evidence that it is a 0% chance. Provide, for example, the number of times in which the coin is flipped where, from there on out it can reach heads no longer. I would be very interested, as that makes no sense at all.

Read Zappa's post.

 

 

 

 

Note: You cannot actually divide by infinity, I added this just for simplicity. Instead of dividing by infinity, you would take the limit of 1/x as x goes to infinity. For those who do not yet know what limits are, basically if x becomes really really really really big, what number does 1/x tend towards?

 

 

 

 

I'm just going to assume you both missed that part of the post...I did indeed prove that if you flipped a coin an infinite amount of times, there is a 0% chance that you would get heads every time.

 

I'll try to explain again, but first, you have to understand what flipping a coin an infinite amount of times means. Infinity is not a number, so when you do something an "infinite amount of times", it means you cannot put a number on the amount of times you flipped that coin, the amount of times it is flipped is never ending.

 

Obviously your idea of "at some point in time it will have to be tails" is ridiculous if you are trying to come up with some type of actual proof. But once again, I will state the logical outcome of flipping a coin an infinite amount of times, and try to explain it better.

 

If you flip a coin, the chances of it landing on heads x times in a row is 1/2^x for x greater than 0. If we are going to perform this task an infinite amount of times, this means we have to take the limit as x approaches infinity of 1/2^x. The limit of this is 0, if you need a proof on limits, go google it.

 

Now you might be saying, "but wait!!, just because the limit is zero doesn't mean it actually reaches 0!!", yes, that is true, but in reality you also never reach infinity, because there is always a number which is bigger than whatever one you are on. 

 

The point is, if you COULD flip a coin for an infinite amount of trials, the probability of having heads for every one of that infinite set of trials would be exactly zero. What you seem to be wanting to know is if there is some specific point where the probability becomes zero, and that point is one infinitely far away, a point which we can never reach in reality.

 

So to clarify things further, doing an infinite amount of trials is just taking a limit, because you can't actually do an infinite amount of trials. The only way to deal with infinities is to use limits, to see what number the function approaches as you approach infinity.

 

And to make things more interesting for you, for x E N ( x is an element of the Natural set of Numbers), for every x, there is a non-zero probability that you will flip heads every time, where x is the number of times you flip the coin. BUT, IF YOU FLIP A COIN AN INFINITE AMOUNT OF TIMES, THE PROBABILITY BECOMES ZERO

 

I hope that will convince you that there is indeed a 0 probability, but then again, I don't think you understand your question yet.

 

"The limit of this is 0, if you need a proof on limits, go google it."

I did, first two sources say you're wrong.

http://www.mathsisfun.com/calculus/limits-infinity.html

https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/liminfdirectory/LimitInfinity.html

You are trying to say the limit to infinity is 0, it is not, and CANNOT be calculated because infinity is not a number.

 

 

To bad you didn't actually read the links you posted, or you might have learned something...Once you finish highschool math, you will learn that you can in fact take limits to infinity. All of calculus is based around this concept. 

 

And in case you still have doubts, you can just use a calculator http://www.wolframalpha.com/input/?i=lim+x-%3Einfinity+1%2Fx.

 

The only real issue you could have with this is that a limit is the number you are approaching, not one you actually ever reach. But it is the same concept as you never actually reaching infinity, because there is no sign that says "Here, this is infinity, you've gone far enough".

 

But when you say you flip a coin an infinite amount of times, then you are just hypothetically saying "what if we could reach infinity", well then, we would also reach 0 probability.

 

1st link http://www.mathsisfun.com/calculus/limits-infinity.html

Question: What is the value of 1/∞ ?

Answer: We don't know!

2nd link https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/liminfdirectory/LimitInfinity.html

In fact, the forms and  are examples of indeterminate forms.

Please show me where both of those articles later contradict themselves.

Edited September 29, 201312 yr by StolenLogic

Even if infinity could be reached, you're all forgetting the 0 is a LIMIT and not an actual value that it will get to.

Just like the graph shows above, the y value value approaches zero indefinitely. It will never reach it, but it is so close we put a name on it called a limit.

 

I don't think any side is "wrong" when it comes to this question because in reality no one knows.

 

 

 

 

I am sorry, but you cannot divide by infinity, because infinity is not a number, it is a concept.

 

 

 

 

 

i'd say it's possible, but near impossible.

I just proved it's impossible! 0% chance, as in it cannot happen

 

Your whole case seems to rest on your belief which you've "simplified" as "any number divided by infinity = 0. "

Which, you pulled out of your ass- It is not factually based, at all. I don't know where you got that from.

You're going to have to provide actual evidence that it is a 0% chance. Provide, for example, the number of times in which the coin is flipped where, from there on out it can reach heads no longer. I would be very interested, as that makes no sense at all.

Read Zappa's post.

 

 

 

 

Note: You cannot actually divide by infinity, I added this just for simplicity. Instead of dividing by infinity, you would take the limit of 1/x as x goes to infinity. For those who do not yet know what limits are, basically if x becomes really really really really big, what number does 1/x tend towards?

 

 

 

 

I'm just going to assume you both missed that part of the post...I did indeed prove that if you flipped a coin an infinite amount of times, there is a 0% chance that you would get heads every time.

 

I'll try to explain again, but first, you have to understand what flipping a coin an infinite amount of times means. Infinity is not a number, so when you do something an "infinite amount of times", it means you cannot put a number on the amount of times you flipped that coin, the amount of times it is flipped is never ending.

 

Obviously your idea of "at some point in time it will have to be tails" is ridiculous if you are trying to come up with some type of actual proof. But once again, I will state the logical outcome of flipping a coin an infinite amount of times, and try to explain it better.

 

If you flip a coin, the chances of it landing on heads x times in a row is 1/2^x for x greater than 0. If we are going to perform this task an infinite amount of times, this means we have to take the limit as x approaches infinity of 1/2^x. The limit of this is 0, if you need a proof on limits, go google it.

 

Now you might be saying, "but wait!!, just because the limit is zero doesn't mean it actually reaches 0!!", yes, that is true, but in reality you also never reach infinity, because there is always a number which is bigger than whatever one you are on. 

 

The point is, if you COULD flip a coin for an infinite amount of trials, the probability of having heads for every one of that infinite set of trials would be exactly zero. What you seem to be wanting to know is if there is some specific point where the probability becomes zero, and that point is one infinitely far away, a point which we can never reach in reality.

 

So to clarify things further, doing an infinite amount of trials is just taking a limit, because you can't actually do an infinite amount of trials. The only way to deal with infinities is to use limits, to see what number the function approaches as you approach infinity.

 

And to make things more interesting for you, for x E N ( x is an element of the Natural set of Numbers), for every x, there is a non-zero probability that you will flip heads every time, where x is the number of times you flip the coin. BUT, IF YOU FLIP A COIN AN INFINITE AMOUNT OF TIMES, THE PROBABILITY BECOMES ZERO

 

I hope that will convince you that there is indeed a 0 probability, but then again, I don't think you understand your question yet.

 

"The limit of this is 0, if you need a proof on limits, go google it."

I did, first two sources say you're wrong.

http://www.mathsisfun.com/calculus/limits-infinity.html

https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/liminfdirectory/LimitInfinity.html

You are trying to say the limit to infinity is 0, it is not, and CANNOT be calculated because infinity is not a number.

 

 

To bad you didn't actually read the links you posted, or you might have learned something...Once you finish highschool math, you will learn that you can in fact take limits to infinity. All of calculus is based around this concept. 

 

And in case you still have doubts, you can just use a calculator http://www.wolframalpha.com/input/?i=lim+x-%3Einfinity+1%2Fx.

 

The only real issue you could have with this is that a limit is the number you are approaching, not one you actually ever reach. But it is the same concept as you never actually reaching infinity, because there is no sign that says "Here, this is infinity, you've gone far enough".

 

But when you say you flip a coin an infinite amount of times, then you are just hypothetically saying "what if we could reach infinity", well then, we would also reach 0 probability.

 

1st link http://www.mathsisfun.com/calculus/limits-infinity.html

Question: What is the value of 1/∞ ?

Answer: We don't know!

2nd link https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/liminfdirectory/LimitInfinity.html

In fact, the forms and  are examples of indeterminate forms.

Please show me where both of those articles later contradict themselves.

 

 

1/infinity is not the same as the limit of 1/x as x-> infinity.

http://gyazo.com/cdab8b26b4dc121cbd1b20bea466666c

 

Your second article also has like 10 questions with limits taken to infinity, and gives solutions to all of them...

 

I think when you said the limit to infinity cannot be calculated, you actually meant you cannot divide by infinity, which is true. We can however take the limit as a variable goes to infinity. And as stated in your first link, the limit of 1/x as x approaches infinity is 0.

 

There are cases where the limit does not exist, but this case of flipping a coin is not one of them, because as I showed in my very first post, the limit is indeed 0

Even if infinity could be reached, you're all forgetting the 0 is a LIMIT and not an actual value that it will get to.

Just like the graph shows above, the y value value approaches zero indefinitely. It will never reach it, but it is so close we put a name on it called a limit.

 

I don't think any side is "wrong" when it comes to this question because in reality no one knows.

 

It will reach zero at a point infinitely far away. It is similar to how we calculate gravitational energy, by using a reference point at an infinite distance away where the potential energy would be equal to zero.

 

It never reaches 0, because it never reaches infinity. If you were to hypothetically flip a coin an infinite amount of times (which is impossible due to the nature of infinity), you could say that the probability of flipping heads every time is zero, because you are calculating a non-finite amount of trials.

 

 

On a more interesting note, we actually do know what happens as you approach an infinite amount of trials. We get this through binomial distribution, and the central limit theorem (I haven't looked into it enough to see what the proofs are, but w/e, they exist), which is kind of like the Law of Large Numbers...I think.

 

Anyways, as your number of trials approaches infinity, the average of all the outcomes will approach the normal distribution, or expected value. So if you flip a coin an infinite amount of times, you will actually get just as many heads as tails, assuming it is a non-weighted coin and there is a 50/50 chance of it landing on either heads or tails. 

 

Of course, if you don't believe the chances of getting heads every time is zero, you'll probably think that is even more absurd...

Edited September 29, 201312 yr by ohhungry

 

Even if infinity could be reached, you're all forgetting the 0 is a LIMIT and not an actual value that it will get to.

Just like the graph shows above, the y value value approaches zero indefinitely. It will never reach it, but it is so close we put a name on it called a limit.

 

I don't think any side is "wrong" when it comes to this question because in reality no one knows.

 

It will reach zero at a point infinitely far away. It is similar to how we calculate gravitational energy, by using a reference point at an infinite distance away where the potential energy would be equal to zero.

 

It never reaches 0, because it never reaches infinity. If you were to hypothetically flip a coin an infinite amount of times (which is impossible due to the nature of infinity), you could say that the probability of flipping heads every time is zero, because you are calculating a non-finite amount of trials.

 

 

On a more interesting note, we actually do know what happens as you approach an infinite amount of trials. We get this through binomial distribution, and the central limit theorem (I haven't looked into it enough to see what the proofs are, but w/e, they exist), which is kind of like the Law of Large Numbers...I think.

 

Anyways, as your number of trials approaches infinity, the average of all the outcomes will approach the normal distribution, or expected value. So if you flip a coin an infinite amount of times, you will actually get just as many heads as tails, assuming it is a non-weighted coin and there is a 50/50 chance of it landing on either heads or tails. 

 

Of course, if you don't believe the chances of getting heads every time is zero, you'll probably think that is even more absurd...

 

Good point. This whole problem really revolves around how you perceive the question.

 

 

Even if infinity could be reached, you're all forgetting the 0 is a LIMIT and not an actual value that it will get to.

Just like the graph shows above, the y value value approaches zero indefinitely. It will never reach it, but it is so close we put a name on it called a limit.

 

I don't think any side is "wrong" when it comes to this question because in reality no one knows.

 

It will reach zero at a point infinitely far away. It is similar to how we calculate gravitational energy, by using a reference point at an infinite distance away where the potential energy would be equal to zero.

 

It never reaches 0, because it never reaches infinity. If you were to hypothetically flip a coin an infinite amount of times (which is impossible due to the nature of infinity), you could say that the probability of flipping heads every time is zero, because you are calculating a non-finite amount of trials.

 

 

On a more interesting note, we actually do know what happens as you approach an infinite amount of trials. We get this through binomial distribution, and the central limit theorem (I haven't looked into it enough to see what the proofs are, but w/e, they exist), which is kind of like the Law of Large Numbers...I think.

 

Anyways, as your number of trials approaches infinity, the average of all the outcomes will approach the normal distribution, or expected value. So if you flip a coin an infinite amount of times, you will actually get just as many heads as tails, assuming it is a non-weighted coin and there is a 50/50 chance of it landing on either heads or tails. 

 

Of course, if you don't believe the chances of getting heads every time is zero, you'll probably think that is even more absurd...

 

Good point. This whole problem really revolves around how you perceive the question.

 

I think the only way to really accurately interpret the question is to say "What outcome do I approach if I flip this coin a lot of times", anything else doesn't really make sense in reality.

You're all idiots pointing out obvious facts. Yes it is possible. If there is a chance, which there is, then of course it's possible. Question answered. This thread is pointless now.

You're all idiots pointing out obvious facts. Yes it is possible. If there is a chance, which there is, then of course it's possible. Question answered. This thread is pointless now.

 

Actually it's not possible, read the thread :P