What is infinity divided by infinity? - Mathematics Stack Exchange
Aug 11, 2012 · I know that $\\infty/\\infty$ is not generally defined. However, if we have 2 equal infinities divided by each other, would it be 1? if we have an infinity divided by another half-as-big infinity, for
Uncountable vs Countable Infinity - Mathematics Stack Exchange
Nov 5, 2015 · My friend and I were discussing infinity and stuff about it and ran into some disagreements regarding countable and uncountable infinity. As far as I understand, the list of all natural numbers is
Does a vertical line have no slope, or infinite slope?
Dec 17, 2024 · I have heard some textbooks that vertical lines have no slope (not a slope of 0 0, rather, no slope at all). However, other textbooks say that the slope of a vertical line is ∞ ∞, where the ∞ ∞ is …
I have learned that 1/0 is infinity, why isn't it minus infinity?
An infinite number? Kind of, because I can keep going around infinitely. However, I never actually give away that sweet. This is why people say that 1 / 0 "tends to" infinity - we can't really use infinity as a …
linear algebra - Invertibility of infinite-dimensional matrix ...
May 3, 2020 · How do you extend your definitions to that case, and how infinite is n n? Assuming n =N n = N, the product of two such matrices is still not always well-defined, take for instance the matrix …
calculus - Does $1.0000000000\cdots 1$ with an infinite number of $0 ...
A decimal representation of a number has digits indexed by natural numbers. Which exactly is the position of that last 1 1? Is it the first after the decimal point? The second? The third? Each digit must …
Can a set be infinite and bounded? - Mathematics Stack Exchange
Aug 7, 2014 · Countability is a different concept altogether. An infinite bounded set can be countable (e.g. all rationals between 0 and 1) or uncountable (e.g. all reals between 0 and 1).
calculus - Infinite limits - Mathematics Stack Exchange
Obviously it depends on the definition of "exists". Some authors explicitly work over the extended real line with ±∞ ± ∞ adjoined, so that such infinite limits do explicitly "exist" as first-class values. But …
When does it make sense to say that something is almost infinite?
4 If "almost infinite" makes any sense in any context, it must mean "so large that the difference to infinity doesn't matter." One example where this could be meaningful is if you have parallel resistors and …
Is it viable to ask in an infinite set about the Cardinality?
Dec 16, 2012 · Can you ask given an infinite set about its cardinality? Does an infinite set have a cardinality? So, for example, what would be the cardinality of $+\\infty$?