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Calculus/prove a theory by assumption

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Expert: - 9/3/2008


Question
when I was at school, many years ago, we would prove mathematical theories by making an assumption (I think the summation of a geometrical progression was one ) My question is "what are the rules regarding when you can use this principle and refresh my memory about how this works"

Answer
You can use it when there is something that is known.

For example, let's say you want to know 4²-6, then a very simple proof might say it's 10 by the assumption that 4²=16.

Another one might be to find n! (n factorial).
We know that 1!=1.  With this assumption, 2!=2*1!=2.
Using this as an assumption, 3!=3*2!=3*2=6.
Assuming 6!=720, 7!=5,040 since 7*720=5,040.  Here are assumption was that 6!=720.

Assuming a=b, you can conclude ac=bc.

They are frequently used in proofs by induction.  You assume a function is true for n=k and prove it for n=k+1, then conclude it is true for all n>=k.

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