if a property holds for rational numbers ,will it also holds for integers Does it holds for whole - Maths - Rational Numbers

Question

if a property holds for rational numbers ,will it also holds
for integers ? Does it holds for whole numbers ? Which will ? Which
will not?

Shridhar Kaushik · Accepted Answer

For the rational numbers, the closure property holds under addition, subtraction and multiplication but not holds under division as '0' is also a rational number and when we will divide some rational by '0', the result will be non-defined value called infinity ( $\infty$ ).

The same is true for integers also i.e. if we take any two integers, then their addition, subtraction and multiplication will again be an integer but the division need not be an integer. Suppose 2 and 3 are integers but $\frac{2}{3}$ is not an integer.

But in case of whole numbers, the closure property holds for addition and multiplication but not holds in case of subtraction since the subtraction of two whole numbers need not be a whole number.

For example, 2 and 5 are whole numbers but 2 – 5 = –3 is not a whole number.

Hence, whole numbers are not closed under subtraction and division.

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if a property holds for rational numbers ,will it also holds for integers ? Does it holds for whole numbers ? Which will ? Which will not?