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annoymage
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Homework Statement
proove is either true of false
let A be a set of integer closed under subtraction. if x and y are element of A, then x-ny is in A for any n in Z.
Homework Equations
n/a
The Attempt at a Solution
is there any proof, without induction?
i suspect its true because any arbitrary positive integer n will satisfy,
though if i try using induction also i stuck.
when n=0, satisfied,
assume it is true for some n>=0
x-(n+1)y=(x-ny)-y, clearly it is inside A
let n>0
x-(-n)y and i don't know how to continue now,
anyway, help me with this induction and also what are other ways without using proof by induction?
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