Question

Show that the closure of $\Bbb{Q}$ is equal to $\Bbb{R}$

score 571 · Answer 1 · 2026-04-14 11:31:17

571

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Show that the closure of $\Bbb{Q}$ is equal to $\Bbb{R}$

Published on 14 Apr 2026 - 11:31

score 1.2k · Answer 2 · 2026-04-15 23:42:28

1.2k

Views

Proving that there is no rational number solution of the equation $x^2-3x+1=0$, extrapolating to a more general problem.

Published on 15 Apr 2026 - 23:42

score 83 · Answer 3 · 2026-05-10 22:02:42

For $x^3+px+q=0$, one of the solutions is $\sqrt 3-1$. Find the value of rational number $p$ and $q$, and other two solutions of the equation.

score 201 · Answer 4 · 2026-04-16 22:39:17

201

Views

defining the value of real numbers raised to rational exponents

Published on 16 Apr 2026 - 22:39

score 779 · Answer 5 · 2026-04-17 02:55:52

779

Views

Find rational numbers $a,b,c$ satisfying $(2^{1/3}-1)^{1/3} = a^{1/3}+b^{1/3}+c^{1/3}$.

Published on 17 Apr 2026 - 2:55

score 914 · Answer 6 · 2026-04-17 11:38:09

914

Views

Is the set $\{(x,y)| x^2+y^2 = \frac{1}{n^2}, n \in \Bbb{N}, x\in \Bbb{Q}$ or $y \in \Bbb{Q}\}$ countable?

Published on 17 Apr 2026 - 11:38

score 220 · Answer 7 · 2026-05-10 17:15:58

220

Views

Representation of rationals as finite continued fractions with restricted coefficients

Published on 10 May 2026 - 17:15

score 177 · Answer 8 · 2026-04-09 05:28:24

177

Views

Find an upper-bound for the denominator of a given expression

Published on 09 Apr 2026 - 5:28

score 71 · Answer 9 · 2026-04-10 09:03:47

71

Views

How would I simplify this rational expression?

Published on 10 Apr 2026 - 9:03

score 1k · Answer 10 · 2026-04-15 18:30:35

1k

Views

Show that any right angled triangle with hypotenuse 1 may be approximated arbitrarily close by one with rational sides

Published on 15 Apr 2026 - 18:30

score 103 · Answer 11 · 2026-05-10 19:23:00

103

Views

What identities collapse number systems?

Published on 10 May 2026 - 19:23

score 15.9k · Answer 12 · 2026-04-30 14:37:02

15.9k

Views

Conjugate of real number

Published on 30 Apr 2026 - 14:37

score 97 · Answer 13 · 2026-03-28 13:39:16

97

Views

Rational point at optimum

Published on 28 Mar 2026 - 13:39

score 986 · Answer 14 · 2026-04-15 03:35:18

986

Views

Proving that the union of two infinite disjoint sets with same cardinality is equipotent with either one

Published on 15 Apr 2026 - 3:35

score 139 · Answer 15 · 2026-04-14 13:48:41

139

Views

Is there any proper way through which we can check whether a number is rational or not

Published on 14 Apr 2026 - 13:48

List Question

Show that the closure of $\Bbb{Q}$ is equal to $\Bbb{R}$

Proving that there is no rational number solution of the equation $x^2-3x+1=0$, extrapolating to a more general problem.

For $x^3+px+q=0$, one of the solutions is $\sqrt 3-1$. Find the value of rational number $p$ and $q$, and other two solutions of the equation.

defining the value of real numbers raised to rational exponents

Find rational numbers $a,b,c$ satisfying $(2^{1/3}-1)^{1/3} = a^{1/3}+b^{1/3}+c^{1/3}$.

Is the set $\{(x,y)| x^2+y^2 = \frac{1}{n^2}, n \in \Bbb{N}, x\in \Bbb{Q}$ or $y \in \Bbb{Q}\}$ countable?

Representation of rationals as finite continued fractions with restricted coefficients

Find an upper-bound for the denominator of a given expression

How would I simplify this rational expression?

Show that any right angled triangle with hypotenuse 1 may be approximated arbitrarily close by one with rational sides

What identities collapse number systems?

Conjugate of real number

Rational point at optimum

Proving that the union of two infinite disjoint sets with same cardinality is equipotent with either one

Is there any proper way through which we can check whether a number is rational or not

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