Question

Is the induction principle still viable if the induction skips over, or does not hold for some numbers?

score 510 · Answer 1 · 2017-03-11 18:31:48

510

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Is the induction principle still viable if the induction skips over, or does not hold for some numbers?

Published on 11 Mar 2017 - 18:31

score 316 · Answer 2 · 2017-03-16 07:54:49

316

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Peano Arithmetic - formulas

Published on 16 Mar 2017 - 7:54

score 135 · Answer 3 · 2017-03-16 09:47:24

135

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peano arithmetic - PA sentences

Published on 16 Mar 2017 - 9:47

score 218 · Answer 4 · 2026-03-26 01:12:16

218

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What is a natural extension of PA that proves the undecidability of the consistency of PA?

Published on 26 Mar 2026 - 1:12

score 163 · Answer 5 · 2017-03-17 15:51:20

163

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Are there meaningful statements about the numbers which cannot be proved with Peano+(independence from Peano)

Published on 17 Mar 2017 - 15:51

score 178 · Answer 6 · 2017-03-20 14:33:14

178

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Let $m,n \in \mathbb{Z}$. Assume $m < n$. Then $m \leq n-1$.

Published on 20 Mar 2017 - 14:33

score 166 · Answer 7 · 2017-03-21 13:51:14

166

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Reflection schema over PA for Rosser provability predicate

Published on 21 Mar 2017 - 13:51

score 2k · Answer 8 · 2017-03-23 04:27:36

2k

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peano arithmetic - addition associativity

Published on 23 Mar 2017 - 4:27

score 82 · Answer 9 · 2017-03-23 06:32:16

82

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How to use nonlogical axioms of Peano Arithmetic

Published on 23 Mar 2017 - 6:32

score 88 · Answer 10 · 2017-03-24 00:32:35

88

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Prove that $(∀m)(∀n)(0 < m \rightarrow (m^− < n^-\leftrightarrow m < n))$

Published on 24 Mar 2017 - 0:32

score 158 · Answer 11 · 2017-03-24 11:04:42

158

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Use Peano Axioms to prove $(∀m)(∀n)(0 < n ⇒ (∃!q)(∃r)(m = q·n + r∧r < n)) $

Published on 24 Mar 2017 - 11:04

score 139 · Answer 12 · 2017-03-24 12:40:47

139

Views

Verification:How can we modifiy principle of function deﬁnition to allow division over the natural numbers?

Published on 24 Mar 2017 - 12:40

score 101 · Answer 13 · 2017-03-24 14:55:08

101

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Verification: Is it the theorem to we need to define the predecessor a natural number?

Published on 24 Mar 2017 - 14:55

score 345 · Answer 14 · 2017-03-25 21:54:16

345

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Peano Axioms for Arithmetic

Published on 25 Mar 2017 - 21:54

score 1.3k · Answer 15 · 2017-03-26 00:17:43

1.3k

Views

Prove cancellation law using peano axioms.

Published on 26 Mar 2017 - 0:17

List Question

Is the induction principle still viable if the induction skips over, or does not hold for some numbers?

Peano Arithmetic - formulas

peano arithmetic - PA sentences

What is a natural extension of PA that proves the undecidability of the consistency of PA?

Are there meaningful statements about the numbers which cannot be proved with Peano+(independence from Peano)

Let $m,n \in \mathbb{Z}$. Assume $m < n$. Then $m \leq n-1$.

Reflection schema over PA for Rosser provability predicate

peano arithmetic - addition associativity

How to use nonlogical axioms of Peano Arithmetic

Prove that $(∀m)(∀n)(0 < m \rightarrow (m^− < n^-\leftrightarrow m < n))$

Use Peano Axioms to prove $(∀m)(∀n)(0 < n ⇒ (∃!q)(∃r)(m = q·n + r∧r < n)) $

Verification:How can we modifiy principle of function deﬁnition to allow division over the natural numbers?

Verification: Is it the theorem to we need to define the predecessor a natural number?

Peano Axioms for Arithmetic

Prove cancellation law using peano axioms.

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