Real Number Definition– As the name says “Real”, so these numbers are actually numbers that really exists. Any number that we think of is considered as a real num, be it positive or negative, fraction or decimal. Real num. are numbers those includes both rational and irrational number. A real-number has to have a value. If there is no value to any number then we can call that number as an imaginary number. All integers like -75, 89, and 84 etc. are considered as real num. All fractions like 3/5, 7/2, -9/7 are considered as real no. too.
Decimals along with repeating decimals are also considered as real num.
These can be any positive or negative number. We can plot All Real Numbers on the number line too. Therefore we can order these numbers and that we cannot do in case of imaginary numbers. The name of imaginary numbers itself says that they are imaginary so we can just imagine them; they do not have a specified value. These numbers can be plotted the same way we plot the integers that is smaller numbers on left and larger numbers on right. So greater the number, more it will be towards right side of number line.
So we can call real nos. as all those numbers which are present on number line are termed as such.
Some Real Numbers Examples are pi, 34/7, 5.676767, -1034, 45.87 etc.
Some examples of imaginary numbers are square root of -34 or square root of -2, as there is a negative under the root, so the value of this number cannot be found.
Similarly value of infinity cannot be determined too .
Hence these numbers are not considered as real and are considered as an imaginary numbers. So these numbers are all integers, fractions decimals and repeating decimals numbers. We can add, subtract, multiply and divide real nos. just like another numbers. We can perform the operations on real-numbers same way as we do them on other numbers.
Now the question arises that Is 0 a Real Number– Zero is considered as an integer and all integers are real-numbers. Therefore zero is considered to be as a real-number.
All Real Numbers Symbol is R which is used by many mathematicians. The symbol R is used to represent the set of real nos. All such numbers can be seen on the number line but we cannot find imaginary numbers on that.