Algebraic Proof(?) That All Real #s=1 by Phaneron

(n=all real #s). (1^2) an infinite amount of times is equal to one. (Sq.Root n) an infinite amount of times reduces to 0.99 repeating, which is the same thing as one. Therefore (1^2) an inf. # of times and (Sq.Root n) an inf. # of times are equal. (I think the ^2 and Sq. can be replaced with infinity instead of having them be infinitely reducing expressions, but let's roll with it- it's the same either way). So if you take away the "infinite # of times" off of both (the replacement I mentioned earlier would work logically for this, not sure about the whole "# of times" thing) you end up with (1^2) = (Sq.Root n). (1^2) = 1. Therefore (Sq.Root n) = 1. (Sq.Root n)^2 = 1^2. Again, it's been established that 1^2 = 1, so now we have (Sq.Root n)^2 = 1. Solving for n, we end up with (n = 1), or all real numbers are equal to one.