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Section 0.2 Manipulating Numbers

This section is included because “it's not crazy until someone says it's crazy”; and hence I would like now to point out that some beliefs about high school mathematics are crazy.

What's the upshot? Well, you might like to know that graduate students also have to go through similar “spirals of understanding”, so you're in good company. The mathematics question-answer site on has even kept a running list of such misconceptions, based off a post from the british mathematician Timothy Gowers in 2015.