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Infinite power tower paradox with e and pi.

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#calculus #number-theory #trigonometry #power-towers
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Seems that I just proved $2=4$.

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#fake-proofs #paradoxes #tetration #power-towers
403
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Power tower inequality

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#inequality #induction #exponentiation #hyperoperation #power-towers
338
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Close power towers

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#inequality #exponentiation #power-towers
603
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Limit involving power tower: $\lim\limits_{n\to\infty} \frac{n+1}n^{\frac n{n-1}^\cdots}$

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#limits #power-towers
920
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how to integrate $\int\underbrace{x^{x^{\cdot^{\cdot^x}}}}_ndx$

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#integration #power-towers
9.1k
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Calculating 7^7^7^7^7^7^7 mod 100

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#number-theory #modular-arithmetic #tetration #power-towers
22.4k
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Can $x^{x^{x^x}}$ be a rational number?

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#number-theory #transcendental-numbers #tetration #power-towers #rationality-testing
665
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Fixed Point of $x_{n+1}=i^{x_n}$

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#complex-numbers #tetration #power-towers
288
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Prove that $F_{2n}(x)=0$ has exactly one root in the interval $x\in(0,1),$ and this root $\to 0$ when $n \to \infty.$

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#calculus #limits #roots #tetration #power-towers
251
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Question involving exponential tower of 19

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#exponentiation #exponential-function #power-towers
6.5k
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What is wrong with this funny proof that 2 = 4 using infinite exponentiation?

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#calculus #algebra-precalculus #exponentiation #fake-proofs #power-towers
672
Views

Convergence of $a_n=(1/2)^{(1/3)^{...^{(1/n)}}}$

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#sequences-and-series #power-towers
149
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On the sequence $(f_n)$ defined by $f_1(x)=x$ and $f_{n+1}(x)=x^{f_n(x)}$

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#analysis #power-towers
241
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Inverse function of $x\mapsto \sqrt[x]x$ on $\left[0,e^{-1}\right]$

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#special-functions #inverse #tetration #lambert-w #power-towers

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