 Mathematical communication follows rules of grammar like any other topic that one can discuss in English. It doesn't matter if you're talking about math or science or history or art or politics or whatever, every sentence you say in English is a sentence and therefore needs to follow all the rules of grammar. So even if a sentence is crawling, crawling with mathematical symbols, even if literally every character in a statement is a mathematical symbol. Take for example, an equation like, take something like x squared plus 2x plus one equals zero. That right there is a mathematical sentence, but it's still a sentence and therefore it requires we follow proper punctuation. So in this video, I just wanna express a very simple but important mathematical writing temp. End each sentence with a period, even when the sentence itself ends with a mathematical symbol or expression. So we just have to put a little period at the end and that then makes it grammatically correct. Take for example, the following sentence. Oiler proved that the sum ranging from k equals one to infinity of one over k to the s is equal to the product over the set of primes of one over one minus one over p squared. That seems like a perfectly good sentence and honestly, this formula would be too complicated to express in words. I read it out loud, but there's a little bit of imprecision when I use my English words that you, a precision that you can be, excuse me, an ambiguity that can be avoided with the mathematical equation right here. But the problem with this sentence is really just the punctuation. There should be a period at the end. I know it's this little simple thing, but if you do that, it'll make your writing much clearer and better composed. Cause after all, why do we have periods when you don't even say periods? You have it so you know that the sentence comes to an end. And so the next thing will continue on where it is. You can need a period to help you understand that this sentence comes to an end. And that's our writing tip for today and brings us to the end of lecture 17. If you learned anything from these videos, please like them, share them with others who might also want to learn this fun mathematics to see more videos like this subscribe in the future. And as always, if you have any questions, please post them in the comments below and I'll be glad to answer them as soon as I can. Bye.