Does 0.999... Equal 1?

[HappySqurriel]

steven787 said:

HappySqurriel said:

You're essentially asking whether the limit of the sequence 0.9 * (0.1^n) is equal to 1 with n starting at 0 and going to infinity ... the answer is yes, but in order to prove it you must first take calculus

The sequence  0.5 * (0.5^n) is also equal to 1 with n starting at 0 and going to infinity

And when you get into number theory you'll find out why that is an oversimplification that we use to express numbers.

 

 

I've taken all the Calculus, Analysis, Number Theory and Linear algebra I ever intend to ...

The problem with a decimal number system and the true nature of numbers is that when you're dealing with an infinitely repeating number (like certain rational and irrational numbers) and you represnet them using a fixed number of decimal places there are an uncountably infinite number of numbers between they number you're representing and the actual underlying number.