Peano Arithmetic

Algebra Level 1

Let S ( ⋅ ) S(\cdot) be the successor function in natural number set N \mathbb N . Compute S ( S ( S ( 0 ) ) ) + S ( S ( S ( S ( S ( 0 ) ) ) ) ) . S(S(S(0)))+S(S(S(S(S(0))))) \; .

You may refer to wiki: Peano axioms .

S ( S ( S ( S ( S ( S ( 0 ) ) ) ) ) ) S(S(S(S(S(S(0)))))) S ( S ( S ( S ( S ( S ( S ( S ( 0 ) ) ) ) ) ) ) ) S(S(S(S(S(S(S(S(0)))))))) S ( S ( S ( S ( S ( S ( S ( 0 ) ) ) ) ) ) ) S(S(S(S(S(S(S(0))))))) S ( S ( S ( S ( S ( S ( S ( S ( S ( 0 ) ) ) ) ) ) ) ) ) S(S(S(S(S(S(S(S(S(0)))))))))

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展豪 張 by 展豪 張 , 22, Hong Kong

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1 solution

I go straightforward! S ( n ) = n + 1 \large S(n) = n +1 → S ( S ( S ( 0 ) ) ) + S ( S ( S ( S ( S ( 0 ) ) ) ) ) →S(S(S(0))) +S(S(S(S(S(0)))))

= 3 + 5 = 8 = S ( S ( S ( S ( S ( S ( S ( S ( 0 ) ) ) ) ) ) ) ) = 3 +5 = 8 = S(S(S(S(S(S(S(S(0))))))))

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Yes. This is a solution using our daily notation. Simply count the number of S ( ⋅ ) S(\cdot)

展豪 張 - 5 years, 1 month ago

It is not a solution. You did not proved that 5 plus 3 is equal eight.

mert sahin - 2 years, 11 months ago

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is this a joke because if it isn't don't be on the site

Kevin Long - 3 months ago

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