Is 3/2 undefined when only considering the natural numbers?

Question

If we only consider the natural numbers, is 3/2 undefined? If not what is the answer?

Answer 1

It depends on what you mean by $3/2$, of course.

But in the usual intepretation where $3/2$ denotes the number such that when it is multiplied by $2$ gives you $3$, then, if you are restricting 'number' to mean 'natural number', then there is no such number.

Answer 2

Kind'a similar analogy... $\sqrt{-1}$ is undefined when considering only real numbers. So mathematicians derived the whole complex number system to give that some meaning.

Its really defining the undefined that has progressed mathematics. So the answer to your question is, 3/2 is defined but only if you extend the natural numbers to a more generalized number system, like positive reals. :)

Answer 3

One never says that the rational number 3/2 is "undefined" as an integer. Rather one simply says that it is nonintegral, or not an integer. On the other hand if 3/2 denotes the value of the (partial) division function on naturals $\rm\:\mathbb N^2\to \mathbb N$ then one may say that this function is undefined at (3,2).