Quick Questions, Short Answers - No Debate

All your questions are related so I'll just take the first one. Unfortunately there is no general method for figuring out whether a number is irrational or not. Usually each number is shown to be irrational in a way that invokes its own specific definition or the context it arises in. For example all proofs of the irrationality of pi basically revolve around the following:1. Generate some specific equation involving the trigonometric functions sin(x), cos(x), tan(x), e.t.c.2. Assume pi is rational.3. The the equation has some property (A), e.g. it's greater than 1.4. It also has property (not A), e.g. it's less than or equal to 1.5. Hence pi being rational is contradictory, so pi is irrational.Step 1 relies heavily on the trigonometric functions, which are related to pi. For other numbers you have to come up with other functions or relations. There is no general method, it's treated on a case by case basis. I think a systematic method of doing this that works in all cases would be a major discovery.

I think it was actually "you", I could be wrong though.In other words:Thou (Nominative singular)
Ye (Nominative Plural)
Thee (Dative/Accusative Singular)
You (Dative/Accusative Plural)

Hi dwise1,Do you happen to know how the accusative plural (you) became the nominative singular form?

So the nominative plural (ye) was replaced by the accusative plural (you) first?Only later did the new nominative plural overcome the singular.A related question actually, if anybody knows the answer, I've been looking on the web, but can't find it. What were the separate dative forms before they merged with the accusative forms? Or would that take you too far back (like Old English)?Edited by Son Goku, : Additional question.