/sci/ - Science & Math

It all boils down to this:

The set of Real numbers is built upon a collection of assumptions or Axioms. One of these axioms is that there are no non-zero infinitesimals. Other sets, like the Integers, make different assumptions.

As soon as someone questions .999...=1, they are questioning the nature of the Real set. The only logical response to this should be to bring up other sets such as the Hyperreals that are capable of presenting meaningful answers to the question.

Instead, many people respond to the question of .999... with something resembling religious fervor. Answers like "1/3x3" or "10x=9.99.." are just insulting because they assume the very axiom of the Real set that is being questioned. It is like using Whole number analysis to prove that 1/2 does not exist! This makes all of higher mathematics look like a scam. The questioner SHOULD distrust people who don't see the problem with those answers - they may be more educated, but they aren't very smart.

It doesn't make any difference whether or not the questioner, or even the answerer has the education to understand Hyperreals. What matters is that the questioner has uncovered something important and (sometimes) useful in mathematics. Such knowledge, even if incomplete, is not to be feared.