Is the proof to my statement correct?

[Mrspi]

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.

 

[The Student]

I thank you for your kind words, but my math education came to a stop about where mathematics was around 1700, and no one in his or her right mind would ever let me teach even college kids. I'd go postal within days. What I am is stubborn; my wife would say that stubborn does not even begin to explain how extremely pig-headed I am.

Mrspi is one of the very best teachers at this site. And she is absolutely right. Sometimes it is best to let your mind rest a bit, and suddenly the light dawns. Henri Poincare, one of the greatest mathematicians of the 19th century, explained that he had worried about a problem for months. He was drafted into the army, and he was putting his foot onto the first step of a bus (horse-drawn no doubt) to go back to the barracks from a leave or a pass when the solution came to him out of the blue. Of course, as he explained, the answer came to him because his mind had been busy with the problem for so long, but he had not consciously worked on the problem for a while. The German chemist, whose name I cannot remember, who discovered the structure of the benzene ring, did so in a dream. It was his unconscious rather than his conscious mind that solved the problem, but his unconscious mind had the advantage of all the work his conscious mind had previously done.

Moreover, I have a vague, perhaps totally mistaken, sense that the adminstrators are getting a bit tired of both of us.

So here is what I propose. First, let's give it a rest for a few days. Second, if and when you want to try again, send me a private message on this site that you want to give it another go. As Mrspi suggested, it may be wise to let it go for months, and perhaps a teacher other than me may be better for YOU. But if you want to try again with me, you and I can pick up through private messages right where we left off, but let's hold off for at least a few days until you you have had some chance to digest some things mentally. Third, if I decide that I am simply not capable of elucidating any further, I shall be honest enough to tell you that. How is that for a proposal?

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.

I will be sure to return the favor for some other educationally hungry soul when I am able to.