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# What does ℕ\{1} mean? watch

1. ive been asked a question on proof by induction. ive been asked to show that when a^n is divided by a-1, its leaves a remainder of 1. where n ∈ ℕ and a ∈ ℕ\{1}.

does ℕ\{1} mean, natural number - 1?

if so does this mean that 'a' can be any whole number bigger than and equal to 0?
2. No, it means any natural number which isn't 1
3. (Original post by SimonM)
No, it means any natural number which isn't 1
oh right, so its any whole number bigger than 1. thanks so much.
4. i dont suppose you know how to solve this question?
5. Induction:

Base case is trivial: a = 1(a-1) + 1
Inductive step: a^(n+1) = a^(n)a = (k(a-1)+1)a = ...
6. I believe that if B is a subset of A, then {A}\{B} is the set of elements of A which are not elements of B.
7. (Original post by tazarooni89)
I believe that if B is a subset of A, then {A}\{B} is the set of elements of A which are not elements of B.
B doesn't need to be a subset of A.
8. (Original post by SimonM)
Induction:

Base case is trivial: a = 1(a-1) + 1
Inductive step: a^(n+1) = a^(n)a = (k(a-1)+1)a = ...
i dont understand how you got these equations and i am unsure where to go from here
9. (Original post by SimonM)
B doesn't need to be a subset of A.
Yeah, good point

I actually meant to write "If B intersects A". But then strictly speaking it probably doesn't even need to do that either
10. (Original post by sarah_vickers)
i dont understand how you got these equations and i am unsure where to go from here
Expand it out, and try to write it in the form m(a-1) +1 for some integer m. (This is what it means to say that it has remainder 1 on division by a-1)

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