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Is fraction the densest subset of real numbers?
No. Fractions do not include irrational numbers. And although there are an infinite number of both rationals and irrationals, there are far more irrational numbers than rationals.
What is the Difference between an integer and a real number?
Integer numbers are a subset of real numbers. Real numbers may contain fractions.
Is real numbers a subset of Integers?
You have it backwards. Integers are a subset of real numbers.
Which is the largest subset of a real numbers?
The real numbers, themselves. Every set is a subset of itself.
What is the relationships among the various number sets in the real number system?
We can look at real numbers as the biggest set. Then some real numbers can be written as fractions. Those are rational numbers and that is a subset of reals. Some cannot be written as fractions and those are irrationals, another subset of the reals.Now those that are rational might have a denominator of 1 such as 3/1 of -3/1. These are a subset of the rationals and hence of the reals. They are called integers. Now if we look at 0 and the positive integers, these are the whole numbers. If we get rid of 0, these are the natural numbers.
