Rolle's Theorem.
Something I first came across at university 40 years ago. It really pissed me off, and still does. Isn't it so totally, utterly obvious that it does not need proving? A bit like claiming that given two numbers, x and x where x
No.
That doesn't prove that there will be a point with slope == 0.
Good Luck! Rich
It still seems totally obvious. And for Rolle's next trick - proving 1+1=2
Agreed. It either starts off directly towards the other point - in which case slope is 0. Or else it starts out at some angle from the straight line between the two points. In which case it has to turn around at some point, which means the slope must go through through 0 (if it is differentiable, as stated).
Only pot smokers rant over such things :-) ...Jim Thompson
I take it you didn't study maths?
Nothing, and I mean *nothing*, is considered so obvious that it doesn't need proving.
"From this proposition it will follow, when arithmetical addition has been defined, that 1+1=2." ? Volume I, 1st edition, page 379 (page 362 in 2nd edition; page 360 in abridged version).
The first rule of mathematics is "assume nothing".
The motto of engineers everywhere is "without assumptions, no progress will be made". This has brought us airplanes (and Langly's Aerodrome), steamships (and the Titanic), the Golden Gate Bridge (and the Tacoma Narrows Bridge), the PC (and the PC), etc.
It was a big impediment to my starting maths at uni. I could not understand why such a thing needed proving.
Well, Rolle's Th is. And it is provably so :-)
I am familiar with that, but maths courses at uni do not *start* with such things.
I did not say I "assumed" it, but that it was totally obvious.
Ah, but then you must *prove* that it is _totally_ obvious, as opposed to say, somewhat obvious, or even mostly obvious...
The proof is too trivial to bother with IMHO
I guess that's the difference between mathematics and engineering. In engineering we have "rules of thumb" and various accepted approximations, perhaps based soley on experience or tradition. In mathematics we strive to have every step and possible loophole explicitly proven and filled in all the way back to the founding axioms, otherwise it's just a guess.
Intuitively obvious to the most casual observer ?:-) ...Jim Thompson
Godel showed that it's just a guess, except in a rather restricted set of mathematics eg Peano arithmetic
We could also impose Sharia, but it wouldn't be my first choice.
Where have _you_ worked? Everywhere that I've ever worked, "That's totally obvious" is the boss's synonym for "I'm making an assumption, and if you question it you're fired".
Would you like some cheese to go with that whine?
Coin toss.
100 times and there is nothing from keeping all 100 from being either heads or tails as each toss has no bearing on subsequent tosses, nor is it affected by any count of previous toss outcomes in the set.Then, there is chaos, of course.
But strangely, after viewing the proof - it's totally obvious.
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