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I am a bit confused to what is a rational and an integer numbers.

These following numbers are integers: $1,2,3,4,... etc.$

but these numbers are also can be written as $\frac{1}{1}, \frac{2}{1}, \frac{3}{1}, \frac{4}{1},... $ and they are called rational numbers, right?

Another example of rational numbers $1.5=\frac{3}{2}$ obviously it is not an integer.

Can integers such as $1,2,3,4,...$ are also be called a set of rational numbers?

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Integers are a subset of rational numbers, meaning all integers are rational numbers, but not all rational numbers are integers.

This Venn diagram shows it best it think (ignoring the fact that there is space outside irrational and rational numbers, because the union of these two sets is the set of reals)

Ryan Shesler
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    nice diagram, except it suggests there are real numbers that are neither rational nor irrational – J. W. Tanner May 12 '19 at 02:37
  • I thought it shows it better than conventional diagrams that have another circle around rational and irrational numbers because of the difference in shape from the real and the rest of the types of number. I will edit my answer to better clarify. @J.W.Tanner – Ryan Shesler May 12 '19 at 02:42