calculus
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
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
I would like to have some examples of infinite dimensional vector spaces that help me to break my habit of thinking of $mathbb{R}^n$ when thinking about vector spaces.
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Is there any pathological shape that has a finite surface area but an infinite volume, sort of like the opposite of a Gabriel''s horn?
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
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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
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
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
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
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
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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
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
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
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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
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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
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
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 ∞ ∞,
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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
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
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