In actuality, when any number (including zero) is multiplied with infinity, then the results are always undefined. Therefore, zero times infinity is undefined. So, zero times infinity is an undefined real number..
Keeping this in consideration, what is the limit of 0 times infinity?
A limit of the form 0 times infinity - Math Central. then both the numerator and denominator approach zero as x approaches infinity. Hence it is a candidate for l'Hospoial's rule.
Additionally, why is division by zero undefined? In ordinary arithmetic, the expression has no meaning, as there is no number which, when multiplied by 0, gives a (assuming a ≠ 0), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 00 is also undefined; when it is the form of a limit, it is an indeterminate form.
In this way, is 0 times infinity indeterminate?
There is no number called "indeterminate", and there is no commonly used number system where multiplying two elements together yields something called "indeterminate". again, with the limit as x approaches c. The limit of f(x) as x goes to infinity is infinity, and the limit of g(x) as x goes to infinity is 0.
Is Infinity equal to zero?
The concept of zero and that of infinity are linked, but, obviously, zero is not infinity. Rather, if we have N / Z, with any positive N, the quotient grows without limit as Z approaches 0. Hence we readily say that N / 0 is infinite.
Related Question Answers
What happens if you multiply by infinity?
Infinity means a number still larger than whatever we can think of. It is therefore obvious that addition and subtraction of a finite number from infinity will have no impact on it and it will still be infinity.What is the value of 1 infinity?
In fact, if you know your precal/calc, you can write this as the limit as x->infinity of 1/x = 0. Essentially, 1 divoded by a very big number gets very close to zero, so… 1 divided by infinity, if you could actually reach infinity, is equal to 0.What is 0 to the power of infinity?
It means that no matter how many times you multiply 0 by 0, you will still end up with 0; which means that, yes, 0^∞=0. Bonus Fact: 1^∞ is also 1, since 1×1=1, and so on, and so forth.Is 1 times infinity an indeterminate form?
For example, the expression 1/0 is undefined as a real number but does not correspond to an indeterminate form, because any limit that gives rise to this form will diverge to infinity. An indeterminate form expression may have a value in some contexts. Note that zero to the power infinity is not an indeterminate form.Can you multiply by infinity?
The problem is that the laws of addition and multiplication you are using hold for natural numbers, but infinity is not a natural number, so these laws do not apply. If they did, you could use a similar argument that multiplying anything by infinity, no matter how small, gives infinity, thus ∞×0=∞.Can you multiply infinity times infinity?
Infinity is a concept of a number so large that we can't conceptualize it. So because infinity is not a number it often does not behave like a number. And if you think of multiplication as just a quicker version of addition you will realize that infinity times infinity is still equal to infinity.Is infinity times 2 bigger than infinity?
So, inf * inf is not bigger than infinity, although 2 ** inf (2 raised to the power of infinity) is actually much larger. Specifically, 2 ** inf is the number of real numbers possible in binary radix, which is the same number as the number of real numbers possible in any radix > 1. Anything to the power of 0 is 1.Can you divide infinity by 2?
Whatever 'infinity divided by 2' should mean, it should be some which, when multiplied by , gives 'infinity'. Unfortunately, there's no way to extend the field operations and still get a field with the extra points, so it's a matter of convention how you define multiplication and division of infinity.What is bigger than infinity to the power of infinity?
So if you asked whether in the extended real line, there was anything greater than infinity to the infinity power, the answer is no, because in the extended real line there is nothing greater than infinity. It's just a matter of definition and doesn't have any special meaning. It is the smallest infinite ordinal.What's infinity divided by infinity?
This equation is obvious incorrect. Therefore, infinity divided by infinity is NOT equal to one. Instead we can get any real number to equal to one when we assume infinity divided by infinity is equal to one, so infinity divided by infinity is undefined.Is zero an infinite number?
That being said, zero CANNOT be infinity because they don't have the same properties. However, there are numbers that we can say are infinite that we can define in terms of other numbers. Zero has a very straightforward relationship to these infinite numbers, because you can make the other numbers out of zero.Is negative infinity over infinity indeterminate?
In both cases the numerator tends to -inf and the denominator tends to +inf, but each case has it's own limit, so there is no rule to determine the limit just by looking at the form ¨negative infinity over infinity¨. There will never be a rule. The magnitude is indeterminate, but the sign is not.Is 0 an even number?
Zero is an even number. In other words, its parity—the quality of an integer being even or odd—is even. This can be easily verified based on the definition of "even": it is an integer multiple of 2, specifically 0 × 2. In this sense, 0 is the "most even" number of all.Can zero be divided by 2?
They say zero divided by anything is zero. However, some say anything divided by zero is undefined, since 4/0 and 5/0 are and so on. For example, 6 divided by 2 is 3, and it can be undone by multiplying 2 by 3 to get 6. If 0/0 is 1, then 1 times 0 is , so it is correct.Can you divide zero?
Division by zero is an operation for which you cannot find an answer, so it is disallowed. You can understand why if you think about how division and multiplication are related. But no value would work for x because 0 times any number is 0. So division by zero doesn't work.Who invented 0?
"Zero and its operation are first defined by [Hindu astronomer and mathematician] Brahmagupta in 628," said Gobets. He developed a symbol for zero: a dot underneath numbers.Can you divide by infinity?
If you divide a thing by infinity, you will get no divisions. Any finite number is just 0 for the infinity because there are always larger than it, it doesn't count at all. So ∞ × 0 = will result into any real number. As for multiplication, the multiplier will still be the same as the quotient.Is zero an integer number?
Integers are whole numbers. Zero, known as a neutral integer because it is neither negative nor positive, is a whole number and thus, zero is an integer.What is the value of 0?
The definition of a number's absolute value is its distance from 0 . Since 0 is zero units away from itself, the absolute value of 0 is just 0 . 
