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Can the hyperreals be used to describe the "gold nuggets" found with nonconverging series and Casimir forces?

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#sequences-and-series #infinity #nonstandard-analysis
341
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Asymptotic behavior of trigonometric functions near infinity

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#complex-analysis #limits #trigonometry #asymptotics #infinity
101
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How to show that $\lim_{x\to 0} (1+x)^{1/x}$ is same as $\lim_{x\to +\infty} (1+1/x)^{x}$?

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#analysis #limits #real-numbers #infinity
105
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Proof that the infinity of all continuous functions is greater than the infinity of reals

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#functions #infinity
625
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The cardinality of the set of transcendental numbers is larger than that of the irrationals.

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#elementary-set-theory #infinity
61
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Has arctangential scale ever introduced in maths before?

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#functions #infinity
152
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Are all the uncountable infinite always greater than countable infinite?

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#elementary-set-theory #infinity
39
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Rules for Arithmetic with Two Equivalent Infinities

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#elementary-set-theory #infinity
104
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How are infinite sets of different cardinalities used practically in everyday life?

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#sequences-and-series #infinity
90
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What is $\infty - 0.5\infty$?

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#limits #infinity
442
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Uniform probability over real numbers?

Published on
#probability-distributions #infinity
272
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Equivalence of Dedekind infinity and infinity, and Axiom of Choice

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#set-theory #infinity #axiom-of-choice
62
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How do I finish this proof proving the divergence of the harmonic series?

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#sequences-and-series #convergence-divergence #infinity #harmonic-functions
3.9k
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How to apply the Abel-summation on this series: $\sum_{k=1}^{\infty}((-1)^{k-1} \cdot k) = 1 - 2 + 3 - 4 + ...$

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#integration #sequences-and-series #infinity #riemann-zeta
1.3k
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What is the real and imaginary part of complex infinity?

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#complex-numbers #complex-geometry #infinity #riemann-surfaces #riemann-sphere

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