Everything feels as if it was randomly defined by the teacher.
I suppose you prefer things randomly defined by Euclid? Just kidding... kinda. Seriously though, randomly defining things and then working through the consequences of that definition is a totally valid way to do math. Those random definitions are called postulates.
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I suppose you prefer things randomly defined by Euclid? Just kidding... kinda. Seriously though, randomly defining things and then working through the consequences of that definition is a totally valid way to do math. Those random definitions are called postulates.
A student may be confused about why just these axions and not some others? It can then be explained that there in fact be alternate set of axions.
But still most teachers give us the same standard set of axions. Why? What would happen if they dropped some of them or replaced them with others?
Euclid's postulates would now be called axioms, not definitions.