0.9999.... = 1.0

[UltimateUnknown]

MDMAlliance said:

Jay520 said:

MDMAlliance said:

Jay520 said:

MDMAlliance said:
.999... =/= 1
It only approximately equals to it. It would be viewed the same way as a number approaches a limit, but never actually touching it. Calculus stuffs.

What number is between 1 and 0.999999...(?)

How is that relevant?  

 

Because if there is no number higher than 0.9999r and less than 1, then the two numbers are of the same value.

There is no "number higher than 0.9999r"  
When you go by that scale, you never reach 1 because you set your limit to 1.  There are an endless amount of points between 0 and 1.

This right here is pretty much the answer. It's setting your limit.

I think I understood the concept of this when looking at the exponential graph (as above), which keeps getting closer and closer to y=0 but never actually touches it. It only touches y=0 at infinity. But if you set the limit for x to infinity, then you can say exp(x)=0. In reality, the graph will never touch the x axis (because we can't really get to infinity) but by setting infinity as your limit you can say it can take a value of 0.

The same thing for the argument of 0.99999.... being equal to 1. If you set the limit for 0.99999... to be 1, then your defined function will be 1 at infinity, just as alliance said.