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alright thanks for watching and today I want to use the intermediate value theorem to show that the function has a fixed point more precisely suppose you have a function f from 0 1 to 0 1 so this just means F is between 0 1 and we are this is continuous then f has a fixed point as a fixed point what does that mean it means there is a specific point think 1/2 such that if you apply F to it then nothing happens so there is is X naught somewhere in the interval 0 comma 1 such that f of X naught equals X naught in other words this point is fixed by F so nothing happens here and there is actually a nice geometric interpretation of this because all that this means is that if you have a function like that from 0 1 2 0 1 for instance like this suppose F looks like this that F must cross the line y equals x kind of like that in other words there must be some point X naught such that the output of X naught is the same thing and Ill give you some kind of neat applications in a second but firs
