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What is infinity divided by infinity? - Mathematics Stack Exchange 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
I have learned that 1 0 is infinity, why isnt 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 number, we can only imagine what we are getting closer to as we move in the direction of infinity
linear algebra - Invertibility of infinite-dimensional matrix . . . 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 whose entries are all 1 1 and multiply it with itself With multiplication somewhat undefined, I just feel a little uneasy about the term "invertible"
sequences and series - What is the sum of an infinite resistor ladder . . . 16 I am trying to solve for the equivalent resistance R∞ R ∞ of an infinite resistor ladder network with geometric progression as in the image below, with the size of the resistors in each section double the size of the previous section
Does a vertical line have no slope, or infinite slope? 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 neither positive nor negative infinity, but an unsigned infinity Which is the right answer? Or, perhaps a better question is, which is more useful? The main reason I am asking this rather
Understanding Euclids proof that the number of primes is infinite . . . This proof is perfectly valid - maybe not as nice as yours, and maybe not what Euclid wrote, but that's by the by Note that the OP was asking specifically for a proof that the number of primes is infinite, not for a proof that if S S is any finite set of primes, then there's a prime not contained in S S
Is there a shape with infinite area but finite perimeter? But the circumference also defines the subset with infinite area that lays "outside" (which is a conventional concept) That other "outside shape" would be an example of a finite-perimeter curve with an infinite area That sounds like cheating and playing with words
Uncountable vs Countable Infinity - Mathematics Stack Exchange 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