I am guessing 0.(9) is 0.999...
It is an integer (1) subtracted by a hypermeme.
whatever brainlet
0.(9) and 1
Michael Turner
Wyatt Young
>It is an integer (1) subtracted by a hypermeme
Which is what type of number?
Daniel Hughes
undefined, which is why assumptions about rounding up to 1 is not correct (but for all real purposes is)
Alexander Lewis
Then how do you define repeating decimals if you don't accept the current definition of repeating decimals?
Nathan Anderson
an infite series never ends. 0.999... does never end. Therefore it never becomes 1.
To make 0.999... equal to 1 you must add a hypermeme number equal to 0.000...1
which does not exist. Theorycrafting about impossible series and their relationship to the real world is a waste of time, which is why brainlet math nerds invent axioms that allow operations on infinite series, to be able to get a result with near infinite precision.
It is not correct to say that 0.999... equals 1 but it works out in the end because there is a limit of how much precision is really necessary.
Kevin Perry
...
Grayson Lee
The notation in the op is such fucking garbage I want to blow my brains out
Alexander Martin
>infinity has a time factor, it's like a steamboat willie cartoon, whistling as it goes
kill yourself
Grayson Gomez
You are retarded and don't know what a limit is. The reason we can't say an infinite sum is equal to anything is because we cannot perform infinitely many operations HOWEVER this is where we can use limits. Limit shows you a bound which your increasing sum/function/whatever cannot increase past. So the limit of 1/2 + 1/4 + ... is 1. When we say sum from 1 to inf of whatever we mean taking the limit of the partial sum 'function'. When people say 0.999... they usually mean the NUMBER they got when they took the limit of 1/2 + 1/4 + ... Keyword here is that they're talking about a number. What you are talking about is a sum which converges to that number and then you claim that 1 converges to itself genius.
9/10 + 9/100 + 9/1000 ... = sum from n=1 to inf of 9/10^n = limit m->inf of 10^-m (10^m - 1) = 0.999...
0.999... is a NUMBER, A BOUND, NOT A PRODUCT.
0.999... = x
9.999... = 10x
9 = 9x
x = 1
0.999 (NUMBER) is the same as 1 (NUMBER).
Grayson Perry
No, you are just as retarded as them.
A real number is an equivalence class from the set of equivalence classes of Cauchy series of rational numbers.
By that definition it instantly follows that 0.999...=1, since being in the same equivalence class is the definition of equality.
>The reason we can't say an infinite sum is equal to anything
Wrong, we can.
>0.999... is a NUMBER, A BOUND, NOT A PRODUCT.
It is an equivalence class of series.
>When people say 0.999... they usually mean the NUMBER they got when they took the limit of 1/2 + 1/4 + ... Keyword here is that they're talking about a number. What you are talking about is a sum which converges to that number and then you claim that 1 converges to itself genius.
The number or the set of equivalence classes are the same, by definition.
>an infite series never ends. 0.999... does never end. Therefore it never becomes 1.
False by definition.