A rational no. is a number represented as p/q, where q and p are integers and q ≠ 0. This States that 0 is a rational number because any number can be divided by 0 and equal 0.
Hence, 0 is a rational number.
Zero can be written as 0=01. We known that, a number of the form pq where p, q are integers and q ≠ 0 is a rational number. So, zero is a rational number.
Hence 0 is a rational, whole, integer and real number but not a natural or irrational number.
We can represents real numbers on line i.e. real line which contains rationals and irrationals. Now by completeness property of real numbers, which says that real line has no gap. So there is no real number that is neither rational nor irrational.
As a whole number that can be written without a remainder, 0 classifies as an integer.
Whole Numbers
{0, 1, 2, 3, 4…..} These include the natural (counting) numbers, but they also include zero. They don't include negatives or fractions, but they can describe how many cows are in a field as well as how many cows remain after they all leave.
Zero is not a fraction or decimal of any number. It is neither positive nor negative. Zero obeys the rule of whole numbers.
Any rational number subtracted from zero is the rational number itself.
Whole Numbers: The numbers 0, 1, 2, . . . . . , N all are called Whole Numbers, i.e. if 0 is included in natural numbers, then it is known as Whole Numbers. Whole numbers are located on the right side of the number line. Zero is the smallest whole number. Also, negative numbers are not whole numbers.
Is '0' a Natural Number? The answer to this question is 'No'. As we know already, natural numbers start with 1 to infinity and are positive integers.
A rational zero is a rational number, which is a number that can be written as a fraction of two integers. An irrational zero is a number that is not rational, so it has an infinitely non-repeating decimal.
The above definitions tell us that 0 is a whole number and not a natural number. The answer is False.
It is undefined because something multiplied by zero gives us zero but there exists no number which when multiplied by zero and the product is 1. This is neither a rational number nor an irrational number.
0 belongs to the sets of whole number, integer, rational number and real number.
Summary: Every integer is a rational number but a rational number need not be an integer.
It is defined that q should not be equal to zero because if it is not so, we can have a fraction of the form finite divided by 0, which will be nothing but not-denied. Hence this condition is imposed to take into consideration only defined fractions.
Explanation: Factually, zero is the rational number that is equal to its negative. This way we've proved that zero is that rational number which is equal to its negative.
Now, whole numbers contain all positive integers starting from 0 to infinity. Whole number is 0, 1, 2, 3, 4, 5……………… and so on. We can see 0 is the whole number but not the natural number. Now, we can say a natural number contains all whole numbers except zero (0).
Whole numbers are all natural numbers including 0 e.g. 0, 1, 2, 3, 4… Integers include all whole numbers and their negative counterpart e.g. …
The whole numbers are the numbers0, 1, 2, 3, 4, and so on (the natural numbers and zero). Negative numbers are not considered "whole numbers." All natural numbers are whole numbers, but not all whole numbers are natural numbers since zero is awhole number but not a natural number.
The number zero as we know it arrived in the West circa 1200, most famously delivered by Italian mathematician Fibonacci (aka Leonardo of Pisa), who brought it, along with the rest of the Arabic numerals, back from his travels to north Africa.
0 (zero) is a number representing an empty quantity. As a number, 0 fulfills a central role in mathematics as the additive identity of the integers, real numbers, and other algebraic structures.
Infinity is not a number, but if it were, it would be the largest number. Of course, such a largest number does not exist in a strict sense: if some number n n n were the largest number, then n + 1 n+1 n+1 would be even larger, leading to a contradiction. Hence infinity is a concept rather than a number.
The smallest integer is zero.