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The concept of infinity comes from division by zero. Imagine you have 15 pencils, you need to divide them into zero people, how much did each person get? It would be nothing! Because nothing is given to them. In mathematics, when you divide any number by zero, it will result in infinity. For example, divide 
by 
, the division will go on forever but you will achieve nothing. The answer will be undefined. Finding the limit of an expression that is divided by zero can be either 
or no limit.
For example, you are asked to find the limit of 
which is approaching 
. Let's replace 
with and find what would we get:
One thing is clear, you will get infinity but what is the sign? Is it either positive infinity or negative infinity? To find that, we will be performing the side limits to determine the sign of 
.
If x has a value that approaches from the left, 
, both the numerator and denominator are negative and the left side limit is: 
.
If x has a value that approaches from the right, 
, the numerator will be negative, the denominator positive and therefore the right-side limit will be: 
.
The next step is to find whether the function has an output on that input. To best way to find that is to check the side limits, if they coincide, that means the function has an output for that input. Since the side limits do not coincide, the function has no limit as 
Example
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Thank you
Thank you Abbas! Good luck with your studies!
With regard to the Zero Over a Number item, is there a mis-statement? It’s immediately followed by “If a number is divided by zero which means that the numerator is zero and the denominator is the number, then the result is zero.”
Hi Mark,
You’re absolutely right to raise the question — there does appear to be a misstatement in that sentence. The phrase “If a number is divided by zero, which means that the numerator is zero and the denominator is the number…” is indeed misleading and should be corrected.
To clarify:
Zero divided by a number (e.g. 0 ÷ 5) equals 0.
A number divided by zero (e.g. 5 ÷ 0) is undefined.
We’ll update the sentence to reflect the correct mathematical explanation. We appreciate you catching that and helping us improve the accuracy of the content!
There is more than one size of infinity, though. What if you multiply the infinity of the whole numbers (Aleph-0) by the infinity of the real numbers (fraktur-c)?
Thanks a lot to you for this essentiol article.
Hi Piyash! Thanks for your comment, great to hear that you found this useful!
Very nice
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