Quote (Hammer_Hdin @ May 18 2010 08:28am)
1/7 in decimal form is an infinitely non-recurring decimal.
The square root of 3 in decimal form is an infinitely non-recurring decimal.
pi in decimal form is an infinitely non-recurring decimal.
Infinitely non-recurring decimals = Irrational numbers
edit: apology accepted, thanks. don't let it happen again.
We don't have to talk about decimal form. ALL THAT MATTERS is whether a number can or cannot be expressed as p/q, for some integers p and q and q is not zero.
The square root of 3 cannot be express as some p/q; thus it is irrational. The same can be said for pi.
BUT 1/7 IS 1/7 (p/q). It is a rational number.
Now here's the thing: your definition agrees with me. And here's where you are wrong: 1/7 IS recurring. Recurring doesn't mean it has to be just one number repeated. It can be a string of numbers. In the case of 1/7, it's 142857 over and over.