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Does .999999999999 (repeated) = 1?

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.9999......is .9999......

Round to get 1 otherwise it'll only get closer to one without actually ever being one

9/9 is 1 not .999999999

 

We talked about this in math actually lol

9/9 is 1 not .999999999

We talked about this in math actually lol

Actually it is equal to 0.999... simply because it is equivalent to 1. Aka 9/9 = 1= 0.999...

For an actual proof lets look at a geometric series expression of 0.999...which can actually be understood with very little background in mathematics.

How can we express 0.999... As a sum of an infinite series of fractions?

This can be done by adding 9/10 + 9/100 + 9/1000 + 9/10000... And so on, with each term being equal to the term previous to it divided by 10. Lets call this series s.

Now lets say we take s, and multiply it by 10. The first term becomes a 9, while the rest of the terms take the place of the term before it.

Such that 10s = 9 + 9/10 + 9/100 + 9/1000 + 9/10000...

Now, if we take our series 10s, and subtract from it the series s, we can then see that every term will be cancelled out except for the 9.

So 10s - s = 9,

9s = 9

s = 1

As you can see from this, our infinite series is equal to 1. And hence 0.999... = 1.

This is essentially the same as a proof Zappa did earlier, but now you can see why the geometric series converges to 1

Note: 0.999... Means 0.999 followed by an infinite amount of 9's

Edited by ohhungry

Yes it does. .99 repeating = 1. I learned a proof for it from a teacher, dont remember the full explanation but basically 1/3 = .33 repeating and 1/3+1/3+1/3=3/3 which is technically .99 repeating, but is 1

9/9 is still 1 by the .9999... logic because of a simple application of geometric series.

This is logically equal to the summation of [9 *(1/10)^n] from n = 1 to infinity.  When that summation is evaluated, the result is 1.

Yes it does, everyone that tried to give a proof that it doesn't failed, and I don't need to give a proof of why it is because there is this site called google.com that you can use to searh to get answers and not post useless threads.

 

PS bump

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