"It is important to realize that there is no mathematics without proofs. You won't be able to learn any mathematics without dirtying your hands and trying out the ideas you learn about in the solutions of problems."
"If you want to know why the tree is growing upside down, ask the computer scientists who introduced this convention.(The conventional wisdom is that they never went out of the room, and they never saw a real tree.)"
"You may wonder why we needed two proofs. Certainly not because a single proof would not have given enough confidence in the truth of the statement! Unlike in a legal procedure, a mathematical proof either gives absolute certainty or else it is useless. No matter how many incomplete proofs we give, t"
"Exercise. We shoot 50 shots at a square target, the side of which is 70 cm long. We are quite a good shot, because all of our shots hit the target. Prove that there are two bulletholes that are closer than 15 cm. Solution: Imagine that our target is an old chessboard. One row and one column of it ha"
"Chess seating in Diane's sense."
"For example, it could easily happen that A CROC BIT SIMON. And it may be true that Napoleon always wanted a TOMB IN CORSICA. It is questionable, but certainly grammatically correct, to assert that COB IS ROMANTIC. Some universities may have a course on MAC IN ROBOTICS. But one would have to write a "
"Lemma 2.5.1 For every x > 0, \[\frac{x - 1}{x} \le \ln(x) \le x - 1\]"
"Primes are strange (as we'll see) and in their irregular sequence, many strange patterns can be observed, which than fail if we move on to larger numbers."