"Not a good test taker..."- I don't understand.

someon
Thu, 09 Jul 2009 06:03:39 +0000

“And all math is based on 1+1=2, a statement which was based on induction. There may be a rare case in the universe where 1+1 doesn’t equal 2.”

No. That is completely false. Most of math is based on ZFC (or more informally, set theory):

[Zermelo?Fraenkel set theory - Wikipedia, the free encyclopedia](Zermelo–Fraenkel set theory - Wikipedia)

And even then, you can create a new system if you want, with different axioms. It does not matter whether these axioms are “true.” In fact, I believe most mathematicians will tell you that it is pointless to discuss the “truth” of these axioms. They are only supposed. THe truth comes in the form on if-then statements.

In fact, it took (sorry I forgot the names) a couple of people interested in the foundations of mathematics (something interesting to wiki) something like 400 pages before they proved that 1+1=2. But, for all intents and purposes, you may consider 2 to be defined as 1+1. That is, if you start with some axioms for reals (or, for torture, start with axioms for integers and construct the reals), one of them is that there is a multiplicative identity, denoted by “1”. 2 may be defined to be the addition of the multiplicative identity to itself.
And math is not based on induction. It is based on deduction using valid rules of inference, which are themselves assumed for the sake of whatever you are doing.

EDIT: Honestly, if you want to talk about foundations of math, the only people who really know what they are talking about most of the time are people who do research in the field.

If you want to talk about knowing things about reality… I’d say that feynman would be a good author to read on the subject. If you want to torture yourself, you could read certain parts of Hume where he talks about empiricism. But maybe I’ll leave one thing: It is not certain that there is an “objective reality” out there. As someone hoping to go into physics though, I sure hope that there is.

To clear something up, I think that what the above two posters meant by mathematical induction is different from what username meant. The former were talking about a particular method of proof while the latter I believe, was talking about the basis for 1+1=2