Is 0.99999999-infinity equal to 1?

Question

If so, please explain how to solve/prove it.

Answer 1

Yes it is

let x = .99999....... 1
10x = 9.99999....... 2

subtract 1st from 2nd

9x = 9
as there are infinite 9s in 1st so infinite in 2nd so they cancell
had there been finite then in second one less
so x = 1

Answer 2

No. something to the 1st capability equals itself. Infinity to the capability of infinity could be taking infinity (an impossibility, when you consider that there is not any ending) and in essence multiplying by utilising itself an limitless volume of circumstances (additionally impossible).

Answer 3

If u do any operations on infinity the answer is always infinity because it is something undefined and everybody has their own infinity. If i say that in my sense infinity is 0.99999999 then the answer would be zero. Hence, we cannot claim the answer to be something when we are subtracting a number which is undefined and does not exists.

Answer 4

Mathametically, It approaces to 1 but not equal to 1.

You have to consider the problem of limits

say for example

Lim x
x ->1

This means 1 is reaching towards 1, but will never be equal to 1. If you consider 0 and 1, there are are infinite points you can find between 0 to 1. Thus even if you have a number 0.99999 until infinity, it will never be equal to 1 mathametically.

cheers:)

Answer 5

They are equal and its not hard to prove if we restate your question a little bit. Instead of talking about .9999-infinity
lets talk first about ".9999-n", where ".9999-n" is the sum .9+.09+.009+,,,. for n terms.

".9999-n" = 9[1/10+1/100+1/1000+...+ 10^(-n)]

".9999-n"/9 = 1/10+1/100+1/1000+...+ 10^(-n)
".9999-n"/90 = 1/100 + 1/1000 + ... + 10^(-n-1)

Note that be subtracting these two, most of the terms cancel.

".9999-n"(1/9-1/90) = 1/10 - 10^(-n-1)
".9999-n"(1/10)= 1/10-10^(-n-1)

".9999-n" = 1 - 10^(-n)

Now we can say that as n becomes larger and larger

lim ".9999-n" as n->infinity = 1

Answer 6

Well, "infinity" is one thing, and "infinitesimal" is another thing... "Infinity" is an infinitely big number, and infinitesimal is an infinitely small number.

So, 0.9999999-infinity is... the negative infinity!

But, from the other answers, I think you wrote it in an unclear way... you should have written "0.9999999..." Then, yes, the answer is that this number is equal to 1, since you can round it. The difference between the number and 1 would be the "infinitesimal" I told about before, and thus the difference can be approached to zero.

So, yes, 0.999999... is equal to 1.

Answer 7

when can we say a real number a is not equal to b? when we can find a real number between a and b.
between 0.999999... to infinity and 1 there is no real number.
So essentially 0.9999... = 1
Mathematically it can be proved as many answerers have done before me.

Answer 8

Yes it is. 0.99999999....infinity is equal to 1.

Reason:

The L.H.S. is evidently the sum of an infinite G.P. with common ratio 0.1 and first term 0.9.

Hence, by using formula for the summation of an infinite G.P.;

We have : L.H.S. = 0.9/(1-0.1) = 0.9/0.9 =1 = R.H.S.

Hope you will give it as a best answer.

Answer 9

This is a pretty famous question, and there are many ways to prove it. See below for some links to information about it:

Answer 10

1/3=0.33333333333....
3*0.3333333333333...=0.99999999....

then,what is (1/3)*3 ?