>>13754713I'm thinking in mathematical terms here, so no need to act like a complete idiot. First off, real numbers are uncountably infinite. You can put any element into a set as you wish, but it still isn't ordered. You can define a total order >= on the real numbers, but it isn't sufficient enough for induction, since you would want a total order such as <=. (since you need to prove a base case such like P(0) )
In other words, you would need to construct a well-order on real numbers. Some say that such an order does not exist (but I haven't seen a proof of this yet) on real numbers, others say it does exist, but it hasn't yet been found.
