It makes sense to work from natural language as examples, after all its out of natural language that mathematical notations is adapted.
P.9: Mathematical language, the ambiguity of simple terms like ‘and’ and ‘is’. It’s important to clearly see the ambiguity and how the mathematical notation helps decrease it.
Sets allow a definition of defining properties to numbers. In an interesting example, we can define all the points in a circle as . This is a way of translating the cartesian space into a set.proabbi
Often its inconvenient to write statements with set notation, but it is useful in some situation, like the geometric one.
When numbers are considered nouns, sets act as a replacement for adjectives. Nouns are constantly shifting in classification depending on context of the statement. Will have to think about this a bit.
Functions
functions as transformations of mathematical objects.
If f(x) is a function then f turns the object x in object y.