The "greatest common divisor" of two integers $x$ and $y$, denoted $\text{gdc}(x,y)$ is the largest natural number that divides both of the integers.

For example, $\text{gdc}(8,12)$ is 4, because:

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TODO understand and explain definition.

The usual definition of a polynomial is over a field as shown at polynomial over a field.

However, there is nothing in the immediate definition that prevents us from having a ring instead, i.e. a field but without the commutative property and inverse elements.

The only thing is that then we would need to differentiate between different orderings of the terms of multivariate polynomial, e.g. the following would all be potentially different terms:while for a field they would all go into a single term:so when considering a polynomial over a ring we end up with a lot more more possible terms.

If the ring is a commutative ring however, polynomials do look like proper polynomials: Section "Polynomial over a commutative ring".

Generalization of a plane for any number of dimensions.

Kind of the opposite of a line: the line has dimension 1, and the plane has dimension D-1.

In $D=2$, both happen to coincide, a boring example of an exceptional isomorphism.

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This is likely because at some point, experiments get more and more complicated, and so people are tempted to say "this is the truth" instead of "this is why we think this is the truth", which is much harder.

But we can't be lazy, there is no replacement to the why.

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