Question

Is it legal to define a function that gives different results for 1.0 and for 1?

score 36 · Answer 1 · 2021-03-13 15:30:19

36

Views

Is it legal to define a function that gives different results for 1.0 and for 1?

Published on 13 Mar 2021 - 15:30

score 241 · Answer 2 · 2021-03-14 13:54:47

241

Views

How to prove rigorously that, for any natural number $n$, the open interval $(n, n+1)$ contains no natural number?

Published on 14 Mar 2021 - 13:54

score 1k · Answer 3 · 2021-03-14 16:35:35

1k

Views

How to prove that if $n > 1$ is a natural number, then $n-1$ is also a natural number?

Published on 14 Mar 2021 - 16:35

score 81 · Answer 4 · 2021-03-17 13:39:47

81

Views

The validity of these two proofs (real analysis).

Published on 17 Mar 2021 - 13:39

score 48 · Answer 5 · 2021-03-18 04:41:03

48

Views

Does there exist two infinite subsets of naturals $A, B$ such that each $n \in A + B$ uniquely determines $a \in A, b \in B$ such that $a + b = n$?

Published on 18 Mar 2021 - 4:41

score 225 · Answer 6 · 2021-03-20 12:02:45

225

Views

Function for which $f(n) = 1$ is true only if n is prime.

Published on 20 Mar 2021 - 12:02

score 93 · Answer 7 · 2021-03-20 19:50:26

93

Views

Induction and well ordering principle

Published on 20 Mar 2021 - 19:50

score 169 · Answer 8 · 2026-03-26 09:18:07

169

Views

A slight generalization of the Sieve of Sundaram that might shed light on the $6n \pm 1$ phenomenon of sequence A002822.

Published on 26 Mar 2026 - 9:18

score 102 · Answer 9 · 2021-03-25 00:05:12

102

Views

Existence of a "densest" sequence with natural density $0$

Published on 25 Mar 2021 - 0:05

score 126 · Answer 10 · 2021-03-29 16:01:57

126

Views

Can I induct on the positive natural numbers?

Published on 29 Mar 2021 - 16:01

score 149 · Answer 11 · 2021-03-31 15:07:25

149

Views

Given any model of ZFC, $M$, is $\omega^M$ really a model of PA? Is any arbitrarily model of PA $\omega^M$ for some $M$?

Published on 31 Mar 2021 - 15:07

score 146 · Answer 12 · 2021-04-01 15:41:42

146

Views

Natural density of integers with certain prime signature

Published on 01 Apr 2021 - 15:41

score 117 · Answer 13 · 2026-03-28 04:34:52

117

Views

A Doubt about Well Ordering Principle and Principle of Mathematical Induction

Published on 28 Mar 2026 - 4:34

score 1.5k · Answer 14 · 2021-04-02 12:49:00

1.5k

Views

$\lim_{n \to \infty}\left(\sqrt[3]{n^3+3n}-\sqrt{n^2-2n}\right) $

Published on 02 Apr 2021 - 12:49

score 134 · Answer 15 · 2021-04-06 14:11:45

134

Views

the number of multisets of positive integers whose sum is n

Published on 06 Apr 2021 - 14:11

List Question

Is it legal to define a function that gives different results for 1.0 and for 1?

How to prove rigorously that, for any natural number $n$, the open interval $(n, n+1)$ contains no natural number?

How to prove that if $n > 1$ is a natural number, then $n-1$ is also a natural number?

The validity of these two proofs (real analysis).

Does there exist two infinite subsets of naturals $A, B$ such that each $n \in A + B$ uniquely determines $a \in A, b \in B$ such that $a + b = n$?

Function for which $f(n) = 1$ is true only if n is prime.

Induction and well ordering principle

A slight generalization of the Sieve of Sundaram that might shed light on the $6n \pm 1$ phenomenon of sequence A002822.

Existence of a "densest" sequence with natural density $0$

Can I induct on the positive natural numbers?

Given any model of ZFC, $M$, is $\omega^M$ really a model of PA? Is any arbitrarily model of PA $\omega^M$ for some $M$?

Natural density of integers with certain prime signature

A Doubt about Well Ordering Principle and Principle of Mathematical Induction

$\lim_{n \to \infty}\left(\sqrt[3]{n^3+3n}-\sqrt{n^2-2n}\right) $

the number of multisets of positive integers whose sum is n

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