Split infinitives and the rule about not ending a sentence with a preposition are all rules in English that actually were borrowed from Latin (where they make more sense). When folks wrote some of the first "grammars" of the English language, they borrowed these rules in order to make English more like Latin. So, while we still hear about these rules today, you won't find them in modern grammar books (at least the one about the prepositions, I don't believe). There is a difference between grammar rules and style issues, too.

And, as for the comment above about English teachers being lax in their teaching, it's more that language is a dynamic, living thing with new variations being created every day. Personally, I like it that way, but others adhere to a more conservative view of grammar and style. There are different ways to communicate (some on this board write in a more academic style, while others are more conversational or colloquial, and others mix the two). All are valid, depending on the audience and situation.

Advanced Grammar lesson is now over, children! (Can you tell I miss teaching grammar?)

Truth