Semi-algebraic set
Imagine you have a box of crayons and you want to draw a picture. Your mom says you can only use certain colors and you can only draw in certain places on the paper. A semi-algebraic set is kind of like that.
But instead of colors and paper, we use numbers and equations. Imagine we have a bunch of equations, like "x + y = 5" and "y - z^2 = 3". These equations tell us where we can draw on our paper. For example, if we plug in x=2 and y=3 into the first equation, we get 2+3=5, which is true. So we can draw a dot at (2,3) on our paper. But if we plug in x=2 and z=1 into the second equation, we get 3-1^2=2, which is not true. So we can't draw a dot at (2,?,1).
A semi-algebraic set is a set of points that satisfy a bunch of these equations. It can have many shapes, like a circle or a square or a funny wiggly shape. But the important thing is that we can draw it using these equations. So we can think of it as a box of crayons with certain rules, but instead of colors, we have equations that tell us where we can draw on our paper.
But instead of colors and paper, we use numbers and equations. Imagine we have a bunch of equations, like "x + y = 5" and "y - z^2 = 3". These equations tell us where we can draw on our paper. For example, if we plug in x=2 and y=3 into the first equation, we get 2+3=5, which is true. So we can draw a dot at (2,3) on our paper. But if we plug in x=2 and z=1 into the second equation, we get 3-1^2=2, which is not true. So we can't draw a dot at (2,?,1).
A semi-algebraic set is a set of points that satisfy a bunch of these equations. It can have many shapes, like a circle or a square or a funny wiggly shape. But the important thing is that we can draw it using these equations. So we can think of it as a box of crayons with certain rules, but instead of colors, we have equations that tell us where we can draw on our paper.
Related topics others have asked about: