Tagged Questions
0
votes
0answers
75 views
what is the exact definition of infinity ?
what is the exact definition of infinity ?
the word infinity is used many many times in maths and in life
sometimes we mean that a something is not limited
also , what is the definition of the ...
0
votes
1answer
112 views
Infinite versus unendlich and double-negation
The German term for infinite is unendlich, which transliterates as non-ending, or non-finite.
This is just word-play but from a constructive point of view, is the shift from a negative to a positive ...
2
votes
3answers
118 views
Number of points on line segment
I know the line segment have a infinite number of points, but i know that exist different kinds of infinity ( $\aleph_0 $). My question is there same number of points on segment of line and entire ...
3
votes
0answers
98 views
Cantor and infinities [closed]
I know we have accepted Cantor's ideas a long time ago and many mathematicians use sets and infinities without ever realizing that thinking about sets and infinities intuitively fails, because there ...
-4
votes
1answer
94 views
Proposed $1-1$ map $\mathbb{R} \to \mathbb{N}$ [closed]
Let $n=0.$ Every time you think of a particular real number $r$, let $n=n+1$ and map $r$ to $n$.
Edit: is this even a "map" according to the definition?
16
votes
1answer
606 views
What did Gauss think about infinity?
I have someone who is begging for a conversation with me about infinity. He thinks that Cantor got it wrong, and suggested to me that Gauss did not really believe in infinity, and would not have ...
2
votes
2answers
171 views
Is $\infty$ enough or do I need to write $+\infty$
This is a question of notation. I have seen in many articles that people often denote $+\infty$ when talking about 'positive infinity' of the real numbers. Is that a convention, or it can be written ...
3
votes
2answers
295 views
Comparing infinite numbers
Suppose you have 2 infinite numbers, say $A$ and $B$.
$A$ is an element of the hyperreals, so that $A$ is greater than every real number.
$B$ is the size of the set of natural numbers, $\aleph_0$
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18
votes
3answers
876 views
Math without infinity
Does math require a concept of infinity?
For instance if I wanted to take the limit of $f(x)$ as $x \rightarrow \infty$, I could use the substitution $x=1/y$ and take the limit as $y\rightarrow 0^+$.
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29
votes
2answers
3k views
Are there any series whose convergence is unknown?
Are there any infinite series about which we don't know whether it converges or not? Or are the convergence tests exhaustive, so that in the hands of a competent mathematician any series will ...
