Such a pest—everything that you know about them has to be proved. And the proofs tell you that everything that you know about them is true.
So waste of time? Not exactly, you need to be sure about these things. Obvious isn't always true when in comes to maths, or anything.
The proofs that you use for integers are pointers to the proofs that you will need to use where things aren't so obvious. That's what maths is all about—making sure that the bloody obvious is true or that you can prove the utterly unlikely and all points between. Or saying that the obvious is terribly wrong.
This is what I hate/love about maths—you can't hide from the truth. You can try, but some git will pull you up. And you are the first judge of whatever crap you're selling.
Comments
New comment
'making sure that the bloody obvious is true or that you can prove the utterly unlikely and all points between. Or saying that the obvious is terribly wrong'
I'm going to remember this...
Cantor?
I just recently watched 'dangerous knowledge' and there is stuff out there that cannot be proven
People ended up in hospitals or killed themselves over this...
New comment
@ji
@marcus
I had to think about that.
So, I think, that you're right—some things cannot be proven [in the sense of a logical proof].
Thankfully, when it comes to integers, we don't run into such problems. Altthough the distribution of the primes is a wee bit tricky
neil