The real number system is a mathematical field.
To start with, the Real number system is a Group. This means that it is a set of elements (numbers) with a binary operation (addition) that combines any two elements in the set to form a third element which is also in the set. The Group satisfies four axioms: closure, associativity, identity and invertibility.
In addition, it is a Ring. A ring is an Abelian group (that is, addition is commutative) and it has a second binary operation (multiplication) that is defined on its elements. This second operation is distributive over the first.
And finally, a Field is a Ring over which division - by non-zero numbers - is defined.
There are several mathematical terms above which have been left undefined to keep the answer to a manageable size. All these algebraic structures are more than a term's worth of studying. You can find out more about them using Wikipedia but be sure to select the hit that has "mathematical" in it!
Real Numbers are the series beginning from 1,2,3....up to infinity. Note that 0 is not a real number , negative values and fractional values are excluded as well. For an in depth understanding on the Real Number System refer to ' The Golden Ratio' by Mario Livio.
Rational and irrational numbers.
The real number are the union of rational and irrational numbers.
the government makes up the school system
An example of contemporary use of real number system in business is a mathematician which his/her job is to come up with the next numbers in the number line which still doesn't have an end. So mathematician will use a number line everyday that they work.
Real numbers are madeup of rational and irrational numbers
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skeletal system makes up frame of the body
In many countries, you will only come across real numbers up to the age of around 16. If you continue to study mathematics beyond that you will find that the number system extends beyond the real numbers: to imaginary and complex numbers, and further still to quaternions.
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the bones.
Muscle of course!