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Sorry if the question has been asked before, but is there any proof that 0.00...1 equals 0?
Or not, as the case may be
Thanks for any replies :)
Or not, as the case may be
Thanks for any replies :)
? Where is the one placed at?0.00...1
Yes, I think people probably realized that's what you meant, but there is no such thing which is why folks are saying that it's undefined. If you get to a point where you can put a 1, then you are not yet at infinity so your statement is nonsensical/undefined.hi, thanks for all your replies. Sorry about not explaining clearing enough.
The "1" is at the end of a length of infinitely many zeros
ie. 0.0000000...(infinte zeros)....1
This is a self-contradiction: if the string of zeros is infinite, it doesn't have an end. That's why that expression doesn't work isn't used in math.The "1" is at the end of a length of infinitely many zeros
ie. 0.0000000...(infinte zeros)....1
That limit is not different from zero. It is precisely zero. As one can see from the epsilon/delta definition of a limit.Perhaps better written as $$\lim_{n\to \infty} \frac{1}{10^n}=0$$
But keep in mind that is the limit. And that is different than zero.
To be picky, one could index the digits in a decimal string over a set of positions with order type omega plus one. The difficulty is not that this is a self-contradiction. The difficulty is that the resulting digit strings do not naturally form an algebraic field.This is a self-contradiction: if the string of zeros is infinite, it doesn't have an end. That's why that expression doesn't work isn't used in math.
Perhaps I should have said the limit is zero but the sequence 1/10, 1/100, ... is never precisely zero.That limit is not different from zero. It is precisely zero. As one can see from the epsilon/delta definition of a limit.
The sequence, which is just a list of numbers, is never precisely anything. This sequence converges to zero, although no element of the sequence is zero.Perhaps I should have said the limit is zero but the sequence 1/10, 1/100, ... is never precisely zero.
I would phrase it that "no term of the sequence is zero".Perhaps I should have said the limit is zero but the sequence 1/10, 1/100, ... is never precisely zero.