Question

Given that $f(x,y)=[x^2+y^2]\frac{x^2y^2}{x^4+y^4}$ and $g(x,y)=[y^2]\frac{xy}{x^2+y^2}$ then find the number of elements in the set E.

score 206 · Answer 1 · 2026-04-17 05:43:58

206

Views

Given that $f(x,y)=[x^2+y^2]\frac{x^2y^2}{x^4+y^4}$ and $g(x,y)=[y^2]\frac{xy}{x^2+y^2}$ then find the number of elements in the set E.

Published on 17 Apr 2026 - 5:43

score 93 · Answer 2 · 2026-04-13 22:35:39

93

Views

What is the cardinality of $^*\mathbb{Q}$?

Published on 13 Apr 2026 - 22:35

score 21 · Answer 3 · 2026-04-13 14:18:20

21

Views

N subset of cardinal number N/2 with minimum pairwise cardinal number of intersections

Published on 13 Apr 2026 - 14:18

score 50 · Answer 4 · 2026-04-14 16:31:12

Let $C[0,1]$ be the set of all continuous function from $[0,1]$ to $\mathbb R$. Prove the cardinality of $C[0,1]$ is equal to that of $\mathbb R$.

score 89 · Answer 5 · 2026-04-11 02:43:32

89

Views

Reducing to regular cardinals in c.c.c. implies same cardinals and cofinalities

Published on 11 Apr 2026 - 2:43

score 48 · Answer 6 · 2026-04-16 15:43:55

48

Views

Every separable metric space has cardinality less than or equal to the cardinality of the continuum

Published on 16 Apr 2026 - 15:43

score 163 · Answer 7 · 2026-04-14 23:35:22

163

Views

Prove that the set of all ternary sequences is uncountable

Published on 14 Apr 2026 - 23:35

score 234 · Answer 8 · 2026-04-14 05:33:46

234

Views

What does it mean "cardinality of a model" and "cardinality of a language" ? Are they the same thing? (Model Theory)

Published on 14 Apr 2026 - 5:33

score 75 · Answer 9 · 2026-04-11 07:46:12

75

Views

Help with proving cardinality equality

Published on 11 Apr 2026 - 7:46

score 35 · Answer 10 · 2026-04-12 19:45:56

35

Views

Help with proving $\mathbb{N} \cong \mathbb{N}^{2}$

Published on 12 Apr 2026 - 19:45

score 137 · Answer 11 · 2026-04-14 15:05:35

137

Views

Does "ZF + no amorphous sets" implies some form of choice?

Published on 14 Apr 2026 - 15:05

score 61 · Answer 12 · 2026-04-14 04:23:23

61

Views

elementary embeddings $j$ in set theory with $V$ and $M$

Published on 14 Apr 2026 - 4:23

score 123 · Answer 13 · 2026-04-17 12:52:12

123

Views

If Replacement Axiom holds in $R(\gamma)$, then $\{\delta<\gamma\mid \delta=\beth_\delta\}$ has size $\gamma$.

Published on 17 Apr 2026 - 12:52

score 108 · Answer 14 · 2026-04-11 21:08:46

108

Views

How many injective functions are there in $\mathbb{N}^\mathbb{N}$?

Published on 11 Apr 2026 - 21:08

score 82 · Answer 15 · 2026-04-16 12:04:09

82

Views

Prove that $|P(\mathbb N) \times P(\mathbb N)| = |(0,1)|.$

Published on 16 Apr 2026 - 12:04

List Question

Given that $f(x,y)=[x^2+y^2]\frac{x^2y^2}{x^4+y^4}$ and $g(x,y)=[y^2]\frac{xy}{x^2+y^2}$ then find the number of elements in the set E.

What is the cardinality of $^*\mathbb{Q}$?

N subset of cardinal number N/2 with minimum pairwise cardinal number of intersections

Let $C[0,1]$ be the set of all continuous function from $[0,1]$ to $\mathbb R$. Prove the cardinality of $C[0,1]$ is equal to that of $\mathbb R$.

Reducing to regular cardinals in c.c.c. implies same cardinals and cofinalities

Every separable metric space has cardinality less than or equal to the cardinality of the continuum

Prove that the set of all ternary sequences is uncountable

What does it mean "cardinality of a model" and "cardinality of a language" ? Are they the same thing? (Model Theory)

Help with proving cardinality equality

Help with proving $\mathbb{N} \cong \mathbb{N}^{2}$

Does "ZF + no amorphous sets" implies some form of choice?

elementary embeddings $j$ in set theory with $V$ and $M$

If Replacement Axiom holds in $R(\gamma)$, then $\{\delta<\gamma\mid \delta=\beth_\delta\}$ has size $\gamma$.

How many injective functions are there in $\mathbb{N}^\mathbb{N}$?

Prove that $|P(\mathbb N) \times P(\mathbb N)| = |(0,1)|.$

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