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Proof by Induction N - Natural number R - Real number (1) Suppose that g: N--->N satisfies g(n+1) = g(n) + g(1) for all n N.

Proof by induction. Attached
Proof by Induction N – Natural number R – Real number (1) Suppose that g : N ---> N satisfies g(n+1) = g(n) + g(1) for all n ɛ N . (a) Find g (0) (b) Show that g(n+m) = g(n) + g(m) for all n , m ɛ N
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Math-8196337.pdf

1g (n + 1) = g (n) + g (1)
Hence
g (1) = g (0 + 1) = g (0) + g (1)
This gives g (0) = 0.
2-For fixed n we have
g (n + m) = g (n + (m − 1) + 1) = g (n + (m − 1)) + g (1)
Hence we inductively,...

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