# how do i prove whether a number is an integer?

• Jun 15th 2012, 07:07 AM
creation1022
how do i prove whether a number is an integer?
is there a way to prove that a number is an integer?
• Jun 15th 2012, 07:22 AM
richard1234
Re: how do i prove whether a number is an integer?
In what context?
• Jun 15th 2012, 03:03 PM
creation1022
Re: how do i prove whether a number is an integer?
in the same way that I can make X a negative;
X <0
Or make X a positive; X>0
How do i make X any integer; X = ???
• Jun 15th 2012, 03:23 PM
Plato
Re: how do i prove whether a number is an integer?
Quote:

Originally Posted by creation1022
in the same way that I can make X a negative;
X <0. Or make X a positive; X>0.How do i make X any integer; X = ???

You are asking a foundational (set theory) question.
This theory is taught in any well constructed Foundation of Mathematics course.
You can get some ideas from this webpage.
• Jun 15th 2012, 04:10 PM
emakarov
Re: how do i prove whether a number is an integer?
Quote:

Originally Posted by creation1022
in the same way that I can make X a negative;
X <0
Or make X a positive; X>0

Writing x < 0 does not make x negative or change x in any way. Rather, for each value of x, the formula x < 0 is true or false. As far as notation goes, you can write $\displaystyle x\in\mathbb{Z}$ or just write "x is an integer"; this statement would be true iff x is an integer. If you need to express the property of being an integer using other concepts, then the answer depends on what you are allowed to use. For example, if you are working with rational numbers and are allowed to use the ceiling function $\displaystyle \lceil\cdot\rceil$, then x is an integer iff $\displaystyle x = \lceil x\rceil$. In the context of set theory see Plato's response.
• Jun 15th 2012, 07:11 PM
richard1234
Re: how do i prove whether a number is an integer?
Or you can show that $\displaystyle x \equiv 0 (mod 1)$.