Welcome to the Alexander Knop's channel, here you may find some small videos for the classes I am teaching. However, they may be useful for people outside of my class.
The fact that you can easily write from right to left made me very confused about the content. It implies that you are from another world and provide some really weird and complicated material.
All you’re doing is repackaging a logical argument. 1. if a line connects two points with no deviation from horizontal, then it is straight 2. if a line connecting two points deviates at any other point resulting in a change from horizontal, then it is not a straight line. 3. A curved line deviates from horizontal and is not a straight line That's geometry and also a scientific law which can be proven. Horizontals are straight lines, not curved. Earth is a plane primarily for this reason alone. Level describes a horizontal line. If all horizontals are parallel to the level horizon, then the horizon will never curve. #thankseuclid
Excellent! Small feedback: calling the two reductio-ad-absurdum rules "negation introduction" clearly only makes sense for one of them. Sticking to calling them RAA seems more intuitive.
Nice video! The binary representation and its xor op took the same teaching time to the theorem proof. I think if we should shorten the former or prolong the latter. For the last part of the proof, we can do one intermediate step to help understand: a' xor b xor c = a' xor (a xor a) xor b xor c = (a' xor a) xor (a xor b xor c) = (0...1rrrrr) xor (0...1rrrrr) = 0. The induction hypothesis should be emphasized (seems mentioned only one time), I felt that the proof assumes the theorem is correct, actually the proof (k+1) assumes (1 to k) are correct.
Your decision to include 7=1 plus 2x2=4 is was made the logic of the statements finally stick in my head. I think you have a gift for explaining these types of things. Keep up the good work.
@zccau if we're going to worry about being so centric on one perspective, the "Islamic golden age" should also really be called the arab-persian golden age. We don't call the Renaissance that happened in Europe the "Christian golden age" for that very reason, yet we don't find it absurd to just generalize all non-Europeans to be lumped together into one thing. It's also wrong for either two to appropriate credit for both renaissances that happened in spite of them, not because of them.
Can someone explain how the grundy function g(x) = 1 for x = 5 (Around video time 6:08)? From my understanding the N(x) = x-1,x-2,x-3. and so N(5) = {4,3,2} and so the mex {4,3,2} is 0.
Ohh so its sort of similar to how when debating you analyse your oppositions thoughts to find logical inconsistencies in the claim or argument they are presenting. I.E are all parts of his/her train of thought consistent with all the other parts. Here its the same thing but the way you find out if the logic is consistent is through mathematics. Am i correct can someone confirm?
