Which of the following are Peano Axioms (as presented in the video). Let N denote the set, s denote the successor function, and 0 denote the selected element. □s is bijective s is surjective □0 € s (N) s(n) = n+1 If UCN then x EU⇒s(x) EU. s is injective □0s (N) □ If UCN with the following properties: (a). Ο EU (b). x EU s(x) EU Then U = N. □ If UCN with the following properties: (a). 0 EN (b). s(x) EU s(x) EU Then U = N.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 38E
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Which of the following are Peano Axioms (as presented in the video). Let N denote the set, s denote
the successor function, and 0 denote the selected element.
s is bijective
s is surjective
□0 € s (N)
s(n) = n+1
If UCN then x EU⇒s(x) EU.
s is injective
□0 s (N)
□ If UCN with the following properties:
(a). 0 EU
(b). x EU⇒s(x) EU
Then U = N.
If U CN with the following properties:
(a). Ο ΕΝ
(b). s(x) EU⇒s(x) EU
Then U = N.
Transcribed Image Text:Which of the following are Peano Axioms (as presented in the video). Let N denote the set, s denote the successor function, and 0 denote the selected element. s is bijective s is surjective □0 € s (N) s(n) = n+1 If UCN then x EU⇒s(x) EU. s is injective □0 s (N) □ If UCN with the following properties: (a). 0 EU (b). x EU⇒s(x) EU Then U = N. If U CN with the following properties: (a). Ο ΕΝ (b). s(x) EU⇒s(x) EU Then U = N.
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