Should we define multiplication as repeated addition?

This article is a comment in my post Math War Over Multiplication which is about the ongoing debate  on whether or not multiplication can be defined as repeated addition. In the article, the author also raises

Mistakes and Misconceptions in Mathematics

Misconceptions are very different from the mistakes students make. Mistakes are not consciously made. Misconceptions are. Mistakes are usually one-off, while misconceptions, the gods forbid, could be for keeps. Mistakes are

Technically, Fractions are Not Numbers

It is misleading to put fractions alongside the sets of numbers – counting, whole, integers, rational, irrational and real. The diagram below which are in many Mathematics I (Year 7)