Question

Which equations support the fact that rational numbers are closed under subtraction?

a) 4.5 - 0.5 = 4

b) 5√4 - √4 = 4√4

c) √8 - √8 = 0

d) 2√3 - √3 = √3

Answer 1

For any set \(\color{black}{\displaystyle \mathbb{D} }\), if \(\color{black}{\displaystyle x,y\in\mathbb{D} }\) and \(\color{black}{\displaystyle \mathbb{D} }\) is closed under substraction, then \(\color{black}{\displaystyle (x-y)\in\mathbb{D}}\).

Answer 2

That is the formal definition of being closed under subtraction.

Answer 3

In other words, for rational numbers to be closed under subtraction, you have to subtract a rational number from another rational number and get a rational number.

Answer 4

So, which of the options supports (not proofs, of course, but, supports) that rational numbers are closed under subtraction?

Answer 5

(I added "not proves" because it is an example, not a proof.)

Answer 6

In option do you subtract rational number from a rational number to get a rational number?

Answer 7

In which option do you subtract rational number from a rational number to get a rational number?