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Why the number 0 has no reciprocal?

Updated: 4/28/2022
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12y ago

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Division by zero is not allowed/defined. So you cannot take 'one over zero', or have zero in the denominator.

Without going too technical, a person might say that 1/0 is infinity, and it sounds good. But if you have a function [say f(x) = 1/x] and take the limit of f(x) as x approaches zero, then f(x) approaches infinity as x approaches from the right, but it approaches negative infinity as you approach from the left, therefore the limit does not exist.

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Q: Why the number 0 has no reciprocal?
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Related questions

Does every number have a reciprocal why?

Every number does not. 0 is a number and it does not have a reciprocal.


Does every real number have a reciprocal?

No, 0 does not have a reciprocal, yet 0 is a real number.


What real number does not have reciprocal?

0 has no reciprocal


Is there any number that does not have a reciprocal?

Only 0 doesn't have a reciprocal


Is the reciprocal of every rational number possible?

No. 0 is rational and has no reciprocal.


Is there a number that has no reciprocal?

Yes, 0.


Does every whole number have a reciprocal?

Not just every whole number. Every number has a reciprocal, even 0. The reciprocal of 0 is undefined.


What number has no reciprocal Why?

0, because division by 0 is not defined.


What is the reciprocal of 911?

The reciprocal of any number (other than 0, which has no reciprocal) is 1 divided by that number. In this case, 1 / 911.(Note: to get the reciprocal of a fraction, just exchange the numerator and the denominator.)


What is the inverse of a whole number?

0 has no inverse. Otherwise it is the reciprocal of the number.


What is the reciprocal of -0.8 -2.5 and 0?

The reciprocal of a number, k, is just 1/k. The other way to look at it is that the product of a number and its reciprocal is one. The reciprocals of -0.8, -2.5, and 0 are -1.25, -0.4, and infinity, respectively.


What is the reciprocal of 0?

what is the reciprocal of 0?well you have to understand that a reciprocal of any number is the number that when multiplied gives 1.ex. reciprocal of 2 is 1/2 because 2x1/2 is 1now understanding that what number can we multiply 0 by to get 10x1 nope0x8 nope0x10000000000000000000000000000000 nopebut what if we consider infinity?infinity isn't big it isn't small it is the endlessness of numbers.and zero is the midway point of the numbers.skipping all of the theory we can understand that the recipricol of 0 is infinity.This is a common perception of the reciprocal of zero. Another common answer, more commonly believed, is that 0's reciprocal is undefined.