>>11051269What the fuck did you just say to me.
Why would that analogy make sense except if your definition of limits was based on describing the syllabus of a course like:
"You learn addition before multiplication"
Therefore it's similar to
"You learn limits before derivatives".
Or is there some deeper analog I'm missing?
I'd say a limit is like when a kids say:
"My guy is 5 cool!"
"MY gjuy is 10 COOL"!
"MY GUY IS INFINITY COOOL!"
It's kind of like saying... it looks like the higher we make this number.. the closer it gets to this thing... so we just 'pretend' that IF we make that number infinitely high.. then it will just BE that thing it's getting closer and closer to.
It's a pretty intuitive thing. It would be what kids would naturally come up with when thinking about things.
The 'special case' of a limit is one in which putting in more.. results in more.. forever.
Say working out.. results in getting stronger.. so the more you work out the stronger you get forever. This can be viewed as a pretty useless but special case of a limit.
The more general idea is.. the more you work out.. the closer you get to some 'theoretical maximum'... Now you can never HIT the theoretical maximum because no one is perfect... but you can get closer and closer... the harder you work.
What a limit does is say.. FINE what if i work INFINITELY HARD.. and the answer is simply.. if you work infinitely hard.. you will be at your theoretical maximum.
ie; as hard work increases.. physique tends to a theoretical maximum. The limit.
