The Natural Numbers and the Peano Axioms
25:08
YouTubeNightwing52
The Natural Numbers and the Peano Axioms
This video constructs the natural numbers through the use of the Peano Axioms. The successor function is discussed and addition is defined with it. After this, various properties such as commutativity, associativity, and the cancellation property are proven. This is the first video in a series about constructing the real number system. If you ...
3.5K viewsMay 26, 2020
Peano axioms Peano Arithmetic
This is the formal mathematical proof for 1 1 = 2 using the Peano Axioms. No fluffy examples, just the logic. The Logic: Successor Function: A foundational rule identifying the next number in a sequence. Recursive Rule: A rule that repeats a process step-by-step to reach a conclusion. "Obvious" is the most dangerous word in mathematics. This proof strips away intuition to show how arithmetic is built from the ground up. Hashtags: #math #logic #PeanoAxioms #STEM #LearnOnTikTok #mathematics | Grav
0:55
This is the formal mathematical proof for 1 1 = 2 using the Peano Axioms. No fluffy examples, just the logic. The Logic: Successor Function: A foundational rule identifying the next number in a sequence. Recursive Rule: A rule that repeats a process step-by-step to reach a conclusion. "Obvious" is the most dangerous word in mathematics. This proof strips away intuition to show how arithmetic is built from the ground up. Hashtags: #math #logic #PeanoAxioms #STEM #LearnOnTikTok #mathematics | Grav
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