Sentence (mathematical logic)

Okay, let's talk about sentences in math. You know how we use words to say something? Well, in math, we use symbols and letters to say something too. These symbols and letters form a sentence in math.

A sentence in math is like a statement. For example, "2+2=4" is a sentence in math. It means that if you have 2 things and add another 2 things, you will end up with 4 things.

But sometimes sentences in math are more complicated. They might have different symbols like "∀" or "∃". These symbols are like little shortcuts that help us say something in a more efficient way. They tell us things like "for all" or "there exists".

Here's an example of a more complicated sentence: "∀x∃y(xy=6)". This sentence means that for every x (which could be any number or letter), there exists a y (which could also be any number or letter) that, when multiplied with x, equals 6. So for example, if we plug in x=2, then there must exist a y that, when multiplied with 2, equals 6. We can check that this is true by solving for y (y=3).

Overall, a sentence in math is just like a sentence in language, but it's made up of symbols and letters and it tells us something about numbers and relationships between them.