Actual Infinity in Reality?

[polymath257]

dude...
1/3 = 0.3333333....
2/3 = 0.6666666....
3/3 = 0.9999999.... = 1

dude, 

1/3 does NOT equal 0.3333333...
2/3 does NOT equal 0.6666666...
3/3 does NOT equal  0.9999999...

you are just staying the same thing. It is wrong for the same reason. There is an infinite amount of 3's, 6's and 9's to the right. So it will NEVER equal the fraction or the whole number. An artifact of a base-10 number system.

Yes, the requirement for an infinite expansion is a relic of base 10 in this case. In base 3, 1/3=.1 after all. But in base 3, 1/10 requires an infinite expansion. In both, the square root of 2 requires an infinite expansion. In all cases, the meaning of the infinite expansion gives the appropriate equality.