What is a conjecture, and how do you state it correctly?
A conjecture is your idea about how to generalize the meaning of a given situation. Sort of a statement about what's really going on.
It's hard to give a specific answer to this question. There are many ways to state a conjecture. It's much easier to give examples.
For example we note in playing around with a calculator that 7 * 1 = 7, 7 * 11 = 77, 7 * 111 = 777, etc.. So we might conjecture that if we multiply 7 by 111...111, where there are n ones, we get 777...777, where there are n seven's. If we didn't know arithmetic, we might think we were onto something here. Of course since we know arithmetic, there's really nothing new in this conjecture.
Or we might observe that when we divide whole numbers by 3 we often get .33333... for the decimal part. Again, if we didn't know arithmetic we might think this was pretty astounding and mysterious, and we might want to investigate to learn more about the patterns involved here.
We'll see more examples in Chapter 1.