WEEKLY WHINE

The FAQs on munbers

Many people have been wondering about munbers: what are they, how do you use them, isn't Theorem 1.10 true for identicality as well. But you've got to avoid some common pitfalls that munber students often encounter. Here now are some questions you've probably asked yourself already.

» What are munbers for, really?
Munbers are for being equal to one another even when they're not the same thing. In other words, equality without identicality.

» What about weighted munbers? What are they for?
They make things more fun.

» But can't you use them to make things equal when they're not equal?
No. For munbers, equality is not transitive. That is, «2, 4» = «4, 6» and «4, 6» = «1, 6», but «2, 4» ≠ «1, 6». However, identicality is transitive. So be careful!

» What is zero minus a munber?
For a munber a, 0 - a ≡ -a ≡ -1a.

» What is one over a munber?
For a munber a, 1/a ≡ a^-1.

» Do munbers cancel?
No. Although a - a = 0, that doesn't mean you can replace a - a with 0. See below.

» Can you substitute munbers?
You can only substitute identical munbers. You can't substitute equal munbers. For example, «1, 5» - «1, 2» is equal to 0, but if you substitute «2» for «1, 2», the result is not equal to 0.

» Why isn't a munber minus itself identical to zero?
Because it isn't. «4, 5» - «4, 5» = «-1, 0 [2], 1».

» Can't you just use sets?
Shut up.