Question

rational number plane vector space or not?

score 246 · Answer 1 · 2014-10-08 06:22:04

246

Views

rational number plane vector space or not?

Published on 08 Oct 2014 - 6:22

score 287 · Answer 2 · 2014-10-11 20:51:50

287

Views

Can a $\mathbf{Q}$-basis of $\mathbf{R}$ be explicitly defined?

Published on 11 Oct 2014 - 20:51

score 1.2k · Answer 3 · 2014-10-12 12:23:35

1.2k

Views

Binary expansions of dyadic rationals in $[0,1]$

Published on 12 Oct 2014 - 12:23

score 49 · Answer 4 · 2026-03-26 02:57:43

49

Views

Can a limit of form$\ \frac{0}{0}$ be rational if the numerator is the difference of transcendental functions, and the denominator a polynomial one?

Published on 26 Mar 2026 - 2:57

score 151 · Answer 5 · 2014-10-15 21:52:03

151

Views

Given $\alpha$, can we always find $\beta$ such that both $\sin(\alpha+\beta)$ and $\sin(\alpha-\beta)$ are rational?

Published on 15 Oct 2014 - 21:52

score 103 · Answer 6 · 2026-03-26 02:57:39

103

Views

As$\ n \to \infty$, can a transcendental function$\ f\left(1+ \frac{1}{n}\right)$ to the power of$\ n$ tend to a rational power of$\ e$?

Published on 26 Mar 2026 - 2:57

score 40 · Answer 7 · 2026-03-26 02:56:25

40

Views

Let$\ \lim_{n\to \infty} \frac{ \ln n}{f(n)}=1$. If$\ a,b,c$ are natural, can we have$\ a^{b+c \ln n}\sim a^{c f(n)}$?

Published on 26 Mar 2026 - 2:56

score 3.6k · Answer 8 · 2014-10-20 20:52:49

3.6k

Views

Is the number 0.2343434343434.. rational?

Published on 20 Oct 2014 - 20:52

score 1.6k · Answer 9 · 2026-03-26 04:29:42

1.6k

Views

Proof that a rational is a repeating decimal.

Published on 26 Mar 2026 - 4:29

score 60 · Answer 10 · 2026-03-29 20:16:30

60

Views

For even integers $a$ and $b$, since $(x^b)^{1/a}$ and $(x^{1/a})^b$ have different domains, does it follow that $x^{b/a}$ is not well-defined?

Published on 29 Mar 2026 - 20:16

score 311 · Answer 11 · 2014-10-25 19:02:40

311

Views

Identify irrational basis of $\mathbb{Q}$-vector space

Published on 25 Oct 2014 - 19:02

score 2.4k · Answer 12 · 2014-10-25 22:18:57

2.4k

Views

Multiplying and adding fractions

Published on 25 Oct 2014 - 22:18

score 52 · Answer 13 · 2014-10-26 13:04:25

52

Views

Prove the result is always a rational number

Published on 26 Oct 2014 - 13:04

score 2k · Answer 14 · 2026-03-28 13:38:37

2k

Views

Subtraction of two repeating decimals

Published on 28 Mar 2026 - 13:38

score 1.6k · Answer 15 · 2026-03-27 21:35:46

1.6k

Views

Can the b-adic representation of rational numbers (by quote notation) be extended to non-terminating expansions?

Published on 27 Mar 2026 - 21:35

List Question

rational number plane vector space or not?

Can a $\mathbf{Q}$-basis of $\mathbf{R}$ be explicitly defined?

Binary expansions of dyadic rationals in $[0,1]$

Can a limit of form$\ \frac{0}{0}$ be rational if the numerator is the difference of transcendental functions, and the denominator a polynomial one?

Given $\alpha$, can we always find $\beta$ such that both $\sin(\alpha+\beta)$ and $\sin(\alpha-\beta)$ are rational?

As$\ n \to \infty$, can a transcendental function$\ f\left(1+ \frac{1}{n}\right)$ to the power of$\ n$ tend to a rational power of$\ e$?

Let$\ \lim_{n\to \infty} \frac{ \ln n}{f(n)}=1$. If$\ a,b,c$ are natural, can we have$\ a^{b+c \ln n}\sim a^{c f(n)}$?

Is the number 0.2343434343434.. rational?

Proof that a rational is a repeating decimal.

For even integers $a$ and $b$, since $(x^b)^{1/a}$ and $(x^{1/a})^b$ have different domains, does it follow that $x^{b/a}$ is not well-defined?

Identify irrational basis of $\mathbb{Q}$-vector space

Multiplying and adding fractions

Prove the result is always a rational number

Subtraction of two repeating decimals

Can the b-adic representation of rational numbers (by quote notation) be extended to non-terminating expansions?

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