The Symbol 0 in the Limits of Functions and Sequences
Krystian Karczyński
Founder and General Manager of eTrapez.
Graduate of Mathematics at Poznan University of Technology. Mathematics tutor with many years of experience. Creator of the first eTrapez Courses, which have gained immense popularity among students nationwide.
He lives in Szczecin, Poland. He enjoys walks in the woods, beaches and kayaking.
When working with limits of functions and sequences, we often encounter various mathematical oddities, such as:
or:
The question is – what do they mean? I often come across completely incorrect opinions like: “at higher levels in mathematics, you can divide by 0”.
However, you need to be aware that the symbol: 
can have many meanings and does not always simply mean “the number zero”. In the symbols I’ve listed, it means the function (or sequence) converges to zero, not exactly the number zero.
For example, in the limit of a sequence:
The symbol…
…means that the limit of the sequence in the numerator and denominator equals 0, not that exactly in the numerator and denominator it is 0 (actually, for any term of the sequence, the numerator and denominator are not exactly 0).
So, there is no division by zero in mathematics, even at some higher, “mystical” levels. Although I heard back when stories about Chuck Norris were popular, that he managed to divide by zero. Twice!
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