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| − | Since you came this far already, here's a math problem for you to try:
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| − | What is 9+10?
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| − | (A) 19 (B) 20 (C) 21 (D) 22 (E) 23
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| − | ==Solution 1==
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| − | Define = satisfying the following axioms
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| − | <math>a=a</math>
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| − | <math>a=b \implies b=a</math>
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| − | <math>a=b, b=c \implies a=c</math>
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| − | Define <math>\mathbb{N}</math>
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| − | <math>0 = \emptyset = \{ \}</math>
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| − | <math>0 \in \mathbb{N}_0</math>
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| − | (note we use <math>\mathbb{N}_0</math> cause I'm one of those <math>0 \notin \mathbb{N}</math> people)
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| − | <math>S(n) := n \cup \{n \}</math>
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| − | <math>n \in \mathbb{N}_0 \implies S(n) \in \mathbb{N}_0</math>
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| − | <math>\forall n \in \mathbb{N}_0, n \not= 0, \exists m \in \mathbb{N}_0 : S(m)=n</math>
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| − | Define +
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| − | <math>a+0=a \forall a \in \mathbb{N}_0</math>
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| − | <math>a+S(b)=S(a+b) \forall a,b \in \mathbb{N}_0</math>
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| − | <math>a+b=b+a</math>
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| − | Name the numbers
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| − | <math>1 := S(0) = \{ 0 \} </math>
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| − | <math>2 := S(0) = \{ 0, 1 \} </math>
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| − | <math>\vdots</math>
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