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Does a set with the following properties hold?

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#elementary-set-theory #real-numbers
1.2k
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Let $a < b $ be real numbers and consider set T = $\mathbb Q \ \cap \ [a,b].$ Show $\sup \ T =b$

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#real-analysis #analysis #proof-verification #proof-writing #real-numbers
45
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Trivial (?) Proof

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#real-numbers
83
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Proving inequality for all real $a$ and $b$.

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#inequality #logarithms #real-numbers #a.m.-g.m.-inequality #jensen-inequality
80
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Uniqueness of real numbers represented as products of integer powers of primes

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#sequences-and-series #limits #real-numbers
1k
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Understanding the philosophy behind the axiomatic definition of reals

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#real-analysis #logic #definition #real-numbers
1.1k
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Binary representation of Cantor set?

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#real-analysis #real-numbers #cantor-set
62
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Maximal length of a finite real sequence

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#sequences-and-series #real-numbers
82
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What does ${\beta} \in \mathbb{R}^{p}$ mean exactly?

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#notation #real-numbers
81
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Bound a natural by two consecutive powers

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#real-analysis #elementary-number-theory #induction #real-numbers #natural-numbers
2.9k
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Euclid's Division Lemma Puzzle

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#real-numbers
191
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Does every ordered divisible abelian group admit an expansion (and how many) to an ordered field?

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#field-theory #real-numbers #ordered-fields #ordered-groups #divisible-groups
258
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Equivalence Class and Cauchy

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#real-numbers #equivalence-relations #cauchy-sequences
1.3k
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Are my arguments correct about limit points of $A=${$m+n\sqrt 2:m,n\in \mathbb Z$}?

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#real-analysis #examples-counterexamples #real-numbers #irrational-numbers #rational-numbers
1.7k
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Prove $0\leq x \leq 1 \implies 0 \leq x^2 \leq x \leq 1 $

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#real-analysis #real-numbers

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