4 ms·
Mwell, I'm not really satisfied by your answer. Both "1" and "0" are well-defined expressions; division is also well-defined, but, in order to avoid logical con
by ced 17y ago
Mwell, I'm not really satisfied by your answer. Both "1" and "0" are well-defined expressions; division is also well-defined, but, in order to avoid logical contradictions, we cannot meaningfully define the division of 1 and 0. To me, that sounds exactly like what you described above, and I thought that the axiom of choice was the analog of the "you can't divide by 0" rule.
- ubernostrum 17y agoMaybe look at it this way: There is no X for which "X / 0" is defined. There are many, many, many X (in fact, potentially all X such that X is a set) for which "X is a member of itself" is defined. In other words, division by zero universally leads to contradiction no matter what you put in for X. But self-membership is perfectly well-behaved for lots and lots of values, and only starts to get troublesome on certain particular cases. This is curious: why should something which works well in many, many cases end up at a contradiction based not on the logical form of the statement, but rather on the particular values we substitute in place of its variables?