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- calculus - What is infinity divided by infinity? - Mathematics Stack . . .
Essentially, you gave the answer yourself: "infinity over infinity" is not defined just because it should be the result of limiting processes of different nature I e , since such a definition would be given for the sake of completeness and coherence with the fact "the limiting ratio is the ratio of the limits", your
- What exactly is infinity? - Mathematics Stack Exchange
Infinity is not a natural number, or a real number: there should be no confusion about that We can use infinity as the upper limit of an integral as shorthand to say that all the reals greater than the lower limit are included - that is a conventional use - along with others involving arbitrarily large numbers
- Types of infinity - Mathematics Stack Exchange
$\begingroup$ "Or that the infinity of the even numbers is the same as that of the natural numbers " - not necessary This depends on your definitions I would argue the infinity of natural numbers is by 1 2 less than the infinity of even numbers (positive, negative and zero) I men, not 1 2 times, but the difference $\endgroup$ –
- limits - Infinity divided by infinity - Mathematics Stack Exchange
When we use straightforward approach, we get $$ \frac{\infty+1}{\infty} = \frac{\infty}{\infty} $$ In the process of investigating a limit, we know that both the numerator and denominator are going to infinity but we dont know the behaviour of each dynamics But if we investigate further we get : $$ 1 + \frac{1}{x} $$ Some other examples :
- One divided by Infinity? - Mathematics Stack Exchange
$\begingroup$ Arithmetic with $\infty$ is usually a convention rather than a piece of mathematics (For example, some mathematicians (in measure theory) take $\infty\cdot 0 = 0$ and reason that this should be the case since $\infty\cdot 0$ represents the "area" of an infinite line in the plane with $0$ width and hence should be $0$ since area = height$\times$ width)
- complex analysis - Infinity plus Infinity - Mathematics Stack Exchange
$\begingroup$ In terms of set theory, it is true that for any infinite power K:k+k=kk=k note that for a=0 : ak=0 and not infinity $\endgroup$ – Belgi Commented Mar 19, 2012 at 19:58
- Is 1 + infinity - Mathematics Stack Exchange
My argument is that if $1 + \infty > \infty$ then there exists a number greater than $\infty$, disproving the concept of infinity, because you can't simply add $1$ to infinity, because infinity is ever increasing So new_infinity would just become "1 + infinity"
- Newest infinity Questions - Mathematics Stack Exchange
The quote from the title of this question comes from The Mathematics of Infinity by T G Faticoni But another source says the opposite: when we are adding $\aleph_0$ to $\aleph_0$, for example, the
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