I came across this basic example of a problem:
Prove by mathematical induction that 1 + 2 + 4 + 8 + 6
What am I supposed to prove, the sum? I don't quite get it, so I decided to dig in to encyclopedia references for help:
In mathematics, a proof is a deductive argument for a mathematical statement.
So a proof is just arguing that the "problem" to the equation is correct? Under what measures confines something as an argument of proof? Anyone can argue anything.
I ended up in axioms:
An axiom, or postulate, is a premise or starting point of reasoning.
So if I "reason and/or argue that my problem is correct" I am "proofing"?
Is that all that means?
So 1 + 2 + 4 + 8 + 6 = 21. Assuming you have elementary addition knowledge, and can add summands together, where is there an argument and why?
Basically, what is the point of "proof" in this situation, and how does the idea of "proofs" in math make its purpose worthwhile?
I mean I have a well open mind, but you can't realistically think everything has a purpose for everything at all times. I don't see any practical understanding or idea on "proofs" that makes me just "get it" and find it useful.