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What does ℕ\{1} mean?

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?
Reply 1
Avatar for SimonM
SimonM
18
No, it means any natural number which isn't 1
Reply 2
Avatar for sarah_vickers
sarah_vickers
OP
SimonM
No, it means any natural number which isn't 1


oh right, so its any whole number bigger than 1. thanks so much.
Reply 3
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sarah_vickers
OP
i dont suppose you know how to solve this question?
Reply 4
Avatar for SimonM
SimonM
18
Induction:

Base case is trivial: a = 1(a-1) + 1
Inductive step: a^(n+1) = a^(n)a = (k(a-1)+1)a = ...
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.
Reply 6
Avatar for SimonM
SimonM
18
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.
Reply 7
Avatar for sarah_vickers
sarah_vickers
OP
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 :confused:
SimonM
B doesn't need to be a subset of A.


Yeah, good point :smile:

I actually meant to write "If B intersects A". But then strictly speaking it probably doesn't even need to do that either :s-smilie:
Reply 9
Avatar for SimonM
SimonM
18
sarah_vickers
i dont understand how you got these equations and i am unsure where to go from here :confused:


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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