Hurkyl: It is all the same. A decimal representation of a number is a polynomial if it terminates and an infinite series if it doesn't. Of course .25 is a polynomial. This isn't worth discussing, I am glad you now have and enriched view of the numbering system we all use. Thank you...
Sorry Hurky, but .9999... is a polynomial of the form
a*(1/10^n) for example 9*(10^-1) + 9(10^-2) + 9(10^-3) + ... to infinity
Sorry Halls of Ivy you are saying then
1 is NOT EQUAL to this Infinite sum .9999...
The Infinite sum converges on 1 and never equals it?!
As you can see this was my 1st post and I am new to this forum. Sorry I stole from nobody. That said. If there is no "at infinity" then how does
1 = .9999...(not infinity??). Either the set of terms is finite (in that case the series is less than one) or the set of terms is infinite and we have...
Well I have a problem with the 1 = .999... thing. Because if this is true it implies that 1/n = 0 when n is "at infinity". Please follow my thinking...
Consider the infinite series:
1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... which EQUALS 1. This follows from the fact that
1 = .9999... because...