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## Main Question or Discussion Point

For example:

$$ y^{2} = 25- x^{2} $$

$$ y = \sqrt{25- x^{2}} , -5\leq x\leq 5 $$

This part: $$ , -5\leq x\leq 5 $$

What is the name of this?If it were a function, it would be the

Other example, the equation:

xy = 1

It would restriction X ∈ ℝ

However, if x ≠ 0 then

y =1/x, x ≠ 0

But then returning to the above equation,

xy = 1, It seems that it would have to have the same restriction x ≠ 0 and not X ∈ ℝ In order to have consistency.

What is the purpose of this topic?

I showed some examples of how I do not have a solid background. I'm not convinced of what I am doing. And I'm not sure how to improve it, but I really want.

Can anyone recommend books to form a solid foundation in mathematics, to feel peaceful with, for example, above questions?

$$ y^{2} = 25- x^{2} $$

$$ y = \sqrt{25- x^{2}} , -5\leq x\leq 5 $$

This part: $$ , -5\leq x\leq 5 $$

What is the name of this?If it were a function, it would be the

**domain**. And for equations, and resolutions of equations, what is the name?Other example, the equation:

xy = 1

It would restriction X ∈ ℝ

However, if x ≠ 0 then

y =1/x, x ≠ 0

But then returning to the above equation,

xy = 1, It seems that it would have to have the same restriction x ≠ 0 and not X ∈ ℝ In order to have consistency.

What is the purpose of this topic?

I showed some examples of how I do not have a solid background. I'm not convinced of what I am doing. And I'm not sure how to improve it, but I really want.

Can anyone recommend books to form a solid foundation in mathematics, to feel peaceful with, for example, above questions?