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Math Help - Proving forall statement

  1. #1
    Junior Member
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    Oct 2008
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    Proving forall statement

    How would you go about proving the following statement

    \forall x \in  \mathbb{N}  ((\forall k : 2 \leq k \leq x) \rightarrow x+k \leq kx)

    Would you use strong induction ?? Could one explain how ?

    thank you
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  2. #2
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    Re: Proving forall statement

    I don't think that induction is needed for this problem. I would prove it as follows:

    Suppose that x is in N, and that k is a number satisfying 2<=k<=x.

    Then, x+k<=x+x=2x<=kx as required.

    The first inequatlity follows from the fact that k<=x and the last inequality follows from the fact that 2<=k.

    Hope this helps!

    Optikal
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