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 Originally Posted by a500lbgorilla
If you say 0 exists, and you say 1 exists, and you say 1 is the immediate successor of 0, then you're allowed to say there is an immediate successor to the immediate successor of 0.
I smell a degree in mathematics.
That sentence is, at its core, the foundation of all math.
I mean, historically, it was the postulate of 1, and the successor was 2 (It was 100 years later that someone "discovered" the number 0), but the successor function was the first mathematical idea.
Originally Posted by oskar
So it probably confuses us for the same reason that it confuses us that 1/3 is 0.3333... and 3/3 is 0.999... and 0.999... = 1 because it's not like it's forever trying to get to 1, it's actually just 1.
Actually, all of the rational numbers are dually stated. for example, 0.299999 (repeating 9) = 0.3 ; .012319999 (repeating 9) = .01232.
Every number has (at least) 2 names.
*note, this is not an artifact of the decimal system, in any base, this phenomenon exists.
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