It can be, but it doesn’t have to be. For example, real numbers can be viewed as a one-dimensional vector space over the field of real numbers. And what even number is? We don"t definine this term. We define real numbers, natural numbers, complex numbers but numbers it self have no well defined meaning.
A vector is a thing that can be added together and scaled in “the intuitive way.” That is, for example, if a and b are numbers and v is a vector, then av + bv = (a+b)v (vector addition distributes over scalar multiplication). The prototypical example is the collection of arrows rooted at the origin on the 2D plane, where addition has a simple geometric interpretation (you put the tail of one vector at the tip of another, the resulting point is the new tip) and scaling is “stretching.” But it really could be anything that adds and scales.
I’ve taken like four or five advanced trigonometry courses and I still can’t really define what trigonometry is. Mathematics is like Andrew Tate’s Hustler University scam. If you take one class, it only exists to prove that you’re a mark and sell you more classes.
I enjoyed the trigonometry unit in my highschool geometry class, but that’s because it was mostly proofs, and those were just philosophy about triangles.
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