Question

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

score 569 · Answer 1 · 2018-07-06 09:03:25

569

Views

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

Published on 06 Jul 2018 - 9:03

score 1.2k · Answer 2 · 2018-07-09 12:41:59

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 09 Jul 2018 - 12:41

score 80 · Answer 3 · 2026-03-25 03:04:33

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 196 · Answer 4 · 2018-07-10 16:05:23

196

Views

defining the value of real numbers raised to rational exponents

Published on 10 Jul 2018 - 16:05

score 776 · Answer 5 · 2018-07-11 12:46:11

776

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 11 Jul 2018 - 12:46

score 911 · Answer 6 · 2018-07-12 10:59:01

911

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 12 Jul 2018 - 10:59

score 217 · Answer 7 · 2026-03-25 03:04:06

217

Views

Representation of rationals as finite continued fractions with restricted coefficients

Published on 25 Mar 2026 - 3:04

score 176 · Answer 8 · 2026-03-21 20:02:12

176

Views

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

Published on 21 Mar 2026 - 20:02

score 68 · Answer 9 · 2018-07-23 04:14:19

68

Views

How would I simplify this rational expression?

Published on 23 Jul 2018 - 4:14

score 1k · Answer 10 · 2018-07-27 09:05:55

1k

Views

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

Published on 27 Jul 2018 - 9:05

score 99 · Answer 11 · 2026-03-25 05:59:49

99

Views

What identities collapse number systems?

Published on 25 Mar 2026 - 5:59

score 15.9k · Answer 12 · 2018-07-30 12:05:52

15.9k

Views

Conjugate of real number

Published on 30 Jul 2018 - 12:05

score 94 · Answer 13 · 2018-07-30 12:14:51

94

Views

Rational point at optimum

Published on 30 Jul 2018 - 12:14

score 983 · Answer 14 · 2018-08-02 09:44:48

983

Views

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

Published on 02 Aug 2018 - 9:44

score 136 · Answer 15 · 2018-08-04 19:19:50

136

Views

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

Published on 04 Aug 2018 - 19:19

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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