Oh...and here's MY interpretation of "proof by induction".....
We've got an ordered set of elements.
We have a proposition (a statement) we hope is true for every element in that set.
Step 1: can we show that proposition is true for ONE element of the set?
Step 2: if we ASSUME that the proposition is true for some ARBITRARY (unspecified) element of the set, is it also true for the NEXT element of the set?
If we know the proposition is true for ONE element of the set, and we can show that whenever it is true for some arbitrary element of the set, then it must be true for the NEXT element, then it must be true for ALL elements of the set which are > than the one element we chose in step 1.
There are tons and tons of resources and examples of mathematical induction. We can't make it "happen" for you....you will need to think and think (and maybe think and think and think and think) about it before it "gels" for you.
Sure, that is fine, and I totally agree with taking a rest. I am just so glad that there are people out there like you on great websites like this one that are so helpful.
Originally Posted by JeffM
I will be sure to return the favor for some other educationally hungry soul when I am able to.