>>41
Numerals represent real numbers, real numbers are defined as the set of limits of Cauchy sequences of rational numbers. It's "pretty fuckin' circular" because it is a DEFINITION. This "argument", if you can call it that, is essentially equivalent to:
Me: Shampoo is something you use to clean your hair.
You: No it's not, but I'm not going to explain why I think it's not.
Me: But the word "shampoo" is defined as "something which is used to clean hair."
You: CIRCULAR LOGIC
>>42
The fact that you don't see a connection between the DEFINITION of the real numbers and the validity of a statement about the real numbers makes me fear you're a middle school student. Let me spell it out for you step by step:
0.999... is a real number.
{0.9, 0.99, 0.999, 0.9999, ... } is a Cauchy sequence of rational numbers which trivially converges to 0.999...
{0.9, 0.99, 0.999, 0.9999, ... } also converges to 1 in the rational numbers.
Ergo 0.999... = 1, because by the definition of convergence, a sequence can converge to only one value.
>>44
"So, the simpletons MISS the point that 0.999... is not just a number as written, but it's a FUNCTION in disguise."
No, it is the limit of a sequence. Numerals do not represent functions. gb2introanalysis, you fucking redcream.