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Prove that ℚ is disconnected as a subset of ℝ

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#real-analysis #metric-spaces #real-numbers #connectedness #rational-numbers
135
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Prove $\lim_{x \to a} f(x)g(x) = \lim_{x \to a} f(x) \lim_{x \to a} g(x)$

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#real-analysis #limits #proof-verification #epsilon-delta
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Can we find any realization of the Bolzano Weierstrass theorem?

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#real-analysis #sequences-and-series
342
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prove uniform convergence?

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#real-analysis #convergence-divergence
63
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How to prove uniform continuity

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#real-analysis
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Rudin Principles of Mathematical Analysis: Chapter 4 problem 18.

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#real-analysis #proof-verification
125
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Check my proof of uniform convergence

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#real-analysis #convergence-divergence
67
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Check my proof of convergence?

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#real-analysis
204
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Putnam 1957, 17th Problem

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#real-analysis #trigonometry #contest-math
238
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Wronskian: How to prove that $W'(t)=\text{tr}(A) W(t)$

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#real-analysis #ordinary-differential-equations
723
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Uniform and pointwise convergence for characteristic functions

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#real-analysis #uniform-convergence #pointwise-convergence
107
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If $f$ has compact support, choose $x_j \to 0$ so that the functions $f(x - x_j)$ are independent

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#real-analysis #functional-analysis #lebesgue-measure
99
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Show that if $\lim(x_n - x_{n-2}) = 0$ then $\lim(\frac{x_n - x_{n-1}}{n}) = 0$

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#real-analysis #sequences-and-series #limits
40
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Creating a contradiction using epsilon. Intermediate Value Theorem Proof.

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#real-analysis #proof-verification
361
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Rudin Principles of Mathematics Analysis: Chapter 4 problem 14

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#real-analysis #proof-verification

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