- #1
cyclogon
- 14
- 0
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?cyclogon said: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.cyclogon said: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.cyclogon said: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.aheight said: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.russ_watters said: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.
jbriggs444 said: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.aheight said: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".aheight said:Perhaps I should have said the limit is zero but the sequence 1/10, 1/100, ... is never precisely zero.
Yes, it is possible for a number to have an infinite number of decimal places. This is known as a repeating decimal and is commonly seen in fractions such as 1/3 = 0.3333....
When we write 0.999...., we are essentially representing the infinite decimal 0.999999999.... which is equal to 1. This is because in the decimal system, there is no number between 0.999.... and 1, so they are considered to be the same value.
No, 0.00....1 can never equal 0. This is because the decimal system follows the rule that the further to the right a digit is, the smaller its value. Therefore, adding an infinite number of zeroes before the 1 does not change its value and it will always be greater than 0.
No, there is no difference between 0.999.... and 1. They are simply two different ways of representing the same value, just like how 1/2 and 0.5 are different representations of the same value.
This concept is relevant in mathematics because it demonstrates the idea of limits and infinite series. It also highlights the importance of understanding different representations of numbers and how they can be equivalent.