12
votes
4answers
421 views

Partitioning the naturals into an infinite number of large sets

Is it possible to partition the positive integers into an infinite number of disjoint large sets ?
0
votes
3answers
180 views

Can countability coexist with infinity?

This question concerns the countability of the real numbers. First I will show how I count the numbers between 0 and 1 on the real line. It is done by reversing digits behind the coma, so that e.g. ...
23
votes
4answers
1k views

Is the statement “1/3 of the natural numbers are divisible by 3” true? Is anything similar to it true?

If we're talking about a finite set of the natural numbers, like those between 1 and 500 or 1 and a million, it seems to me that the fraction of numbers in that finite set that have a factor of 5 ...
1
vote
1answer
660 views

Proving that there is no biggest number

Problem Elsewhere, I have seen it proposed by a mathematician that there is a "greatest number", as opposed to infinitely many numbers. This number is supposed to be exceedingly large, larger than ...
1
vote
1answer
192 views

$\frac{-1}{0}$ is infinity or -infinity? [duplicate]

Possible Duplicate: Division by $0$ I was solving a question for my brother today when i got this doubt, i I arrived at the answer as $\frac{-1}{0}$ Will the answer be infinity since ...
-2
votes
4answers
356 views

Golden ratio powers tend to integer values

If $G$ is the golden ratio, then $\lim_{n \to \infty}G^n$ tends ever nearer to integer values that approach $\infty$. Can it therefore be proved that $\infty$ is itself an integer? If not, why not?
17
votes
10answers
5k views

Do infinity and zero really exist?

I'm not going to prove something, this is just a question. From the first day which I went to University until now I had some root problems in some basic mathematical assumptions and concepts. Please ...