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Why are positive rational numbers countable but real numbers are not?

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#discrete-mathematics #real-numbers #infinity #irrational-numbers
345
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Interchange summation (outer infinite, inner dependent on outer)

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#summation #infinity
624
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absolutely integrability implies function approaches zero at positive infinity

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#improper-integrals #infinity
1.8k
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What is wrong with this infinite sum

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#number-theory #summation #infinity
2.7k
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Is it irrational?

Published on
#number-theory #real-numbers #infinity
103
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Concept similar to extended real line in higher dimensions?

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#real-numbers #infinity
386
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Approximating end behavior of a function by plugging in infinity

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#limits #infinity #euler-mascheroni-constant
273
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Prove that $\lim _{x\to \infty \:}(1+\frac{x^x}{x!})^{\frac{1}{x}} = e$

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#limits #factorial #infinity
35
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How to count the number of rebound cycles of a ball in a 1d system after time t, where velocity doubles every rebound

Published on
#infinity
42
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Infinite non deviating slope

Published on
#systems-of-equations #infinity
352
Views

Guests leaving Hilbert's Hotel?

Published on
#soft-question #infinity
93
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What is $\lim\limits_{x \to \infty} \dfrac{x}{x-1}$?

Published on
#limits #infinity
198
Views

Proof of $+\infty=-\infty$ (Maybe)

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#infinity
1.1k
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Infinite limit of trigonometric function

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#calculus #infinity
2.5k
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Is the Cartesian product of two countably infinite sets also countably infinite?

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#elementary-set-theory #proof-verification #infinity

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