The pi lie (or quantum uncertainty)

Great Debates
141

You’re confusing the actual number itself with the representation of the number. To paraphrase a famous painting:

1 <- This is not the number one.

What you’re talking about has to do with how we write the number 1/3, which really has nothing to do with mathematics, or the values of numbers, at all.

142

Third edition made armor classes go positive. D20+stat bonus (Usually strength), + magic bonus + base attack bonus (Roughly, 20- your old THACO… that is, a 5th level fighter would have a BAB of +5, a 5th level wizard would have a BAB of about 2), versus a target number that is the opponent’s Armor Class. Much easier!

Anyhow, it’s very simple. One in twenty, minimum. Considering that, while not all infinities are the same size, they are both infinities, then a AC of infinity versus a sword +infinity would clearly be equal. You have to roll equal or better to hit. If you had to roll greater, it would be one in twenty, but since you merely have to roll equal, it’s nineteen in twenty.

143

But what if we had 6-digit fingers instead of 5-digit fingers? Then we’d probably be counting in base 12 instead of base 10, and 1/3 would be represented as 0,4 (i.e. finite, according to your definition). The fact that 1/3 has an infinite amount of decimals has nothing to do with the number itself, only our way of denoting it.

PS. the inverse of pi is pi^-1, or about 0,318. Just FYI. :slight_smile: DS.

144

I ahvent read the thread and this has probably been mentioned but, in maths, we CAN prove a proterty for an infinite set.

If we can prove that the property holds true for the first example, AND we prove that it holds true for any n+1 example PROVIDING in holds true for example N, THEN it must hold true for all examples. Proof by Mathematical Induction.

145

Well, yes. :slight_smile: But that’s only because you’ve made induction axiomatic. (Peano’s fifth.)

146

Shalmanese, that doesn’t work for any infinite set, only those that are ordered by the natural numbers (not all infinite sets can be ordered this way).

Libertarian, you don’t actually have to make induction axiomatic. You can start with the standard (ZFC) set theory axioms and actually construct a set that satisfies Peano’s axioms.