Question

What are some terms that you use in your everyday life that are really hard to define, yet they're incredibly important and frequently used? How could you explain why undefined terms become so important when we start to write proofs in geometry?

Answer 1

Any expression, like "you're pulling my leg", or "there's more than one way to skin a cat." It's really hard to explain these things to people who haven't grown up with these expressions. Also, words like "the", "and", and others are super important in everyday life, but you really can't describe. Undefined terms are also important in geometry. A point is an undefined term, and so is a line. But without these two things, geometry would be impossible.

Hopefully this helps! Let me know if you have any more questions.