Question

How do I prove formally that for all natural numbers $a\cdot S(c)=b\cdot S(c)\implies a\cdot c=b\cdot c$

score 77 · Answer 1 · 2026-03-30 00:21:23

77

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How do I prove formally that for all natural numbers $a\cdot S(c)=b\cdot S(c)\implies a\cdot c=b\cdot c$

Published on 30 Mar 2026 - 0:21

score 142 · Answer 2 · 2022-05-14 21:40:41

142

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Numbers preceded by perfect cube and followed by perfect square

Published on 14 May 2022 - 21:40

score 62 · Answer 3 · 2022-05-15 03:07:19

62

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What exactly is zero?

Published on 15 May 2022 - 3:07

score 25 · Answer 4 · 2022-05-16 22:29:04

25

Views

Does the infinite limit probability of additive closure for pairs of elements from $(0, 1, 2 \cdots, n)$ not exist?

Published on 16 May 2022 - 22:29

score 81 · Answer 5 · 2026-03-30 00:21:30

81

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If I define addition in the following way, how can I prove that it's commutative?

Published on 30 Mar 2026 - 0:21

score 252 · Answer 6 · 2022-05-23 20:11:34

252

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Contradiction of axioms of real numbers

Published on 23 May 2022 - 20:11

score 60 · Answer 7 · 2026-03-30 00:24:29

60

Views

How do I prove that $\forall a \forall b(\neg a<b\iff b\leq a)$

Published on 30 Mar 2026 - 0:24

score 36 · Answer 8 · 2026-03-30 00:21:15

36

Views

How to prove that $\forall a \forall b \exists x(a+x=b \lor b+x=a)$

Published on 30 Mar 2026 - 0:21

score 146 · Answer 9 · 2022-05-28 23:55:21

146

Views

Why is the axiom of infinity defined as it is?

Published on 28 May 2022 - 23:55

score 187 · Answer 10 · 2026-03-28 13:04:35

187

Views

Prove without the well ordering principle that no m exists such that $n < m < n + 1$ for positive integers $m$ and $n$.

Published on 28 Mar 2026 - 13:04

score 186 · Answer 11 · 2022-06-04 06:19:37

186

Views

proving an inequality for all natural numbers

Published on 04 Jun 2022 - 6:19

score 214 · Answer 12 · 2022-06-07 12:59:40

214

Views

When does the square root of $f:\mathbb{N} \rightarrow \mathbb{N}$ exist?

Published on 07 Jun 2022 - 12:59

score 101 · Answer 13 · 2026-03-30 02:07:14

101

Views

I was able to "prove" by induction that $\forall n \in \mathbb{N} (n\geq 2 \implies n!>2^n)$. Where did I go wrong?

Published on 30 Mar 2026 - 2:07

score 78 · Answer 14 · 2022-06-12 02:14:25

78

Views

Is this an adequate proof that any non-empty subset of N has a minimal element?

Published on 12 Jun 2022 - 2:14

score 40 · Answer 15 · 2026-03-30 02:08:58

40

Views

Can I use a addition table with infinite length and height to define addition on the natural numbers rather than Peano's Axioms?

Published on 30 Mar 2026 - 2:08

List Question

How do I prove formally that for all natural numbers $a\cdot S(c)=b\cdot S(c)\implies a\cdot c=b\cdot c$

Numbers preceded by perfect cube and followed by perfect square

What exactly is zero?

Does the infinite limit probability of additive closure for pairs of elements from $(0, 1, 2 \cdots, n)$ not exist?

If I define addition in the following way, how can I prove that it's commutative?

Contradiction of axioms of real numbers

How do I prove that $\forall a \forall b(\neg a<b\iff b\leq a)$

How to prove that $\forall a \forall b \exists x(a+x=b \lor b+x=a)$

Why is the axiom of infinity defined as it is?

Prove without the well ordering principle that no m exists such that $n < m < n + 1$ for positive integers $m$ and $n$.

proving an inequality for all natural numbers

When does the square root of $f:\mathbb{N} \rightarrow \mathbb{N}$ exist?

I was able to "prove" by induction that $\forall n \in \mathbb{N} (n\geq 2 \implies n!>2^n)$. Where did I go wrong?

Is this an adequate proof that any non-empty subset of N has a minimal element?

Can I use a addition table with infinite length and height to define addition on the natural numbers rather than Peano's Axioms?

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