We can say that zero divided by 1 equals zero and we can also say that this is "defined" as well.
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 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. Some people find these points to be confusing. These notes may be useful for anyone with questions about dividing by 0.
Dividing 0 by any number will give us a zero. Zero will never change when you multiply or divide any number by it. For example, a person has zero toffees which are to be divided among 7 ( let's say) children. This means that there is nothing to be shared or distributed among 7 children.
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).
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.
Infinity is not a number. When we divide one number by another we must get, again, a number; say, real numbers. Since infinity is not a number, it does not make sense to say 0/0 = infinity. Think of a/b to be the number c such that a=bc.
Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Zero divided by zero is zero.
But 'limit' (1/x); x->0 is well defined and is equal to infinity (it is the basic concept of limits). Now this statement is most commonly (though not correctly) referred to as 1/0 = infinity and is so common in mathematics and physics that people working/studying in this field take limits to be obvious.
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 Modern Zero
Around 1200 AD, Italian mathematician Fibonacci introduced zero in Europe. Initially, zero was called 'Sunya' in India, it was called 'Sifr' in the middle east when it reached Italy, it was named 'Zefero' and later in English, it was called 'Zero'.
Since any number multiplied by zero is zero, the expression 0/0 is also undefined; when it is the form of a limit, it is an indeterminate form.
something/0:
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.
Although the concept of infinity has a mathematical basis, we have yet to perform an experiment that yields an infinite result. Even in maths, the idea that something could have no limit is paradoxical. For example, there is no largest counting number nor is there a biggest odd or even number.
∞0 is an indeterminate form, that is, the value can't be determined exactly.
Factorial of a number in mathematics is the product of all the positive numbers less than or equal to a number. But there are no positive values less than zero so the data set cannot be arranged which counts as the possible combination of how data can be arranged (it cannot). Thus, 0! = 1.
The answer depends on which notion of infinity we use. The infinity of limits has no size concept, and the formula would be false. The infinity of set theory does have a size concept and the formula would be kind of true. Technically, statement 2∞ > ∞ is neither true nor false.
Continuity. In numerology, the number 8 means a continuous cycle. On its side, the number 8 becomes the infinity symbol, which signifies the continuous cycle between the beginning and the end.
Answer: Evaluate the value of 5 divided by infinity. Hence, 5 divided by infinity is 0. Alternatively, we know that any number divided by 5 is equal to 0. Therefore, 5 divided by 0 is 0.
0/0 has a special name in the context of limits. It's called an indeterminate form, and it pops up a lot in advanced Math, along with other indeterminate forms like infinity/infinity. Just know that 0/0 can be any number you want it to be. Think of it like this. Let 0/0 = x.
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.
The above form is not possible because 6 is not equal to 0. Therefore, any number when divided by 0 is undefined except for 0. Therefore, the result when 6 is divided by 0 is undefined. Note: We have seen that any number when divided by 0 is undefined except for 0.
Answer and Explanation:
Any number divided by infinity is equal to 0.
Calculators generally return the answer infinity when the result is above the largest finite number that the calculator can calculate and display; typically slightly less than 10^1000.