Zero is the additive identity and since it can be added to any number without changing the number's identity. But zero has some special properties when it comes to multiplication and division. When multiplying a number by 0 it makes the product equal zero, so the product of any real number and 0 is 0.
The rule is that anything multiplied by 0 is equal to 0. Remember this rule, and all multiplication by 0 problems will become instantly easier. If you see 0 in your multiplication problem, then your answer is 0. It doesn't matter where your 0 is located.
No matter how big the number is, when you multiply it with zero, the answer is always simple—zero.
Considering normal arithmetic, it is not possible to divide by zero. This is because "dividing by x" is really just a shorthand way of saying "calculating the amount which gives the original when multiplied by x". Since multiplying by zero always gives zero, we really cannot divide anything non-zero by zero.
Again, any number multiplied by 0 is 0 and so this time every number solves the equation instead of there being a single number that can be taken as the value of 00. In general, a single value can't be assigned to a fraction where the denominator is 0 so the value remains undefined.
Multiplying a number by 0 makes the product equal to zero. Remember that the product of any real number and 0 is 0. For any real number m, m⋅0 = 0. As per the zero property of multiplication, the product of any number and zero (0), is 0.
It is undefined. The rule that zero times anything is zero applies only to objects that are part of the numbering system. Undefined values are not part of the numbering system.
As much as we would like to have an answer for "what's 1 divided by 0?" it's sadly impossible to have an answer. The reason, in short, is that whatever we may answer, we will then have to agree that that answer times 0 equals to 1, and that cannot be true, because anything times 0 is 0. Created by Sal Khan.
These notes discuss why we cannot divide by 0. The short answer is that 0 has no multiplicative inverse, and any attempt to define a real number as the multiplicative inverse of 0 would result in the contradiction 0 = 1.
7 Answers. 0⋅0=0 because a⋅0=0, which is an axiom of multiplication in Peano arithmetic.
Brahmagupta, an astronomer and mathematician from India used zero in mathematical operations like addition and subtraction. Aryabhatta introduced zero in 5th century and Brahmagupta introduced zero in calculations in around 628 BC.
The number 0 is the smallest non-negative integer. The natural number following 0 is 1 and no natural number precedes 0. The number 0 may or may not be considered a natural number, but it is an integer, and hence a rational number and a real number (as well as an algebraic number and a complex number).
The Bodmas rule follows the order of the BODMAS acronym ie B – Brackets, O – Order of powers or roots, D – Division, M – Multiplication A – Addition, and S – Subtraction. Mathematical expressions with multiple operators need to be solved from left to right in the order of BODMAS.
We can say that the division by the number 0 is undefined among the set of real numbers. $\therefore$ The result of 1 divided by 0 is undefined. Note: We must remember that the value of 1 divided by 0 is infinity only in the case of limits. The word infinity signifies the length of the number.
In short, the multiplicative identity is the number 1, because for any other number x, 1*x = x. So, the reason that any number to the zero power is one ibecause any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1.
Summary: Zero divided by 1 is 0.
Any number divided by infinity is equal to 0. To explain why this is the case, we will make use of limits. Infinity is a concept, not an actual number, so we can't just divide a number by infinity.
The thing is something divided by 0 is always undefined because the value has not been defined yet. So, when do we say this something divided by 0 is infinity? Of course, we have seen these a lot of time but why do we say this? Well, something divided by 0 is infinity is the only case when we use limit.
Let's recall the important notes we learned in this discussion. Infinity is not a real number and is only used as a representation for an extremely large real number. Dividing 1 by infinity is equal to zero.
The reason that the result of a division by zero is undefined is the fact that any attempt at a definition leads to a contradiction. a=r*b. r*0=a. (1) But r*0=0 for all numbers r, and so unless a=0 there is no solution of equation (1).
Every integer divides 0. Proof. Let n be an integer. Then 0 = 0 · n, so that n divides 0.
Just like in this example, there's no way to divide a number by zero in math. Or, at least, a way to do so doesn't currently exist. Mathematicians are always trying to find answers to interesting math problems—and plenty of people have tried to work out how to divide by zero.
Because multiplying by infinity is the equivalent of dividing by 0. When you allow things like that in proofs you end up with nonsense like 1 = 0. Multiplying 0 by infinity is the equivalent of 0/0 which is undefined.
One can argue that 0/0 is 0, because 0 divided by anything is 0. Another one can argue that 0/0 is 1, because anything divided by itself is 1. And that's exactly the problem!
Infinity is not a number, but a concept. We can define infinity as the object that is larger than any other number, but infinity is not a real number itself, since it doesn't fulfill the same axioms that the real numbers do.