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Troubles with Indeterminate Symbols (VIDEO)
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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.
This post is kind of a response to a question in the comments on the above YouTube video ( link to the comment ):
I don’t understand something and I need an explanation, why do you simplify “n”? I mean that n/n is an indeterminate symbol (infinity over infinity) help because I’m already lost with this
Understanding what indeterminate symbols REALLY are can be quite tricky. There are also many questions about what you “can” and “can’t” do with them.
A Quick Review
Let’s recall them first:
As you’ve surely heard many times with indeterminate symbols:
– The symbol doesn’t represent any “number” or any mathematical object, but it SYMBOLIZES diverging to infinity (infinity is not a number!)
– The symbol
– The symbol
– The indeterminate symbol
– etc.
So, when we have to calculate the limit:
…we can say that we have an indeterminate symbol
In the expression
In the expression
So we have to use some methods (in this case, pulling out the common factor – which I described in my Limits Course), work around it, etc.
But let’s take a trivial limit:
This is also a limit where we have an indeterminate symbol
In the expression
We CAN perform simplifications in the expression
‘n’ is indeed a mathematical variable on which you can perform arithmetic operations, simplify, etc. (unlike the symbol
In Summary
You can’t perform arithmetic operations, simplify, etc., on the indeterminate symbols
You can perform mathematical operations, simplify, etc., on expressions from which we calculate the limits of sequences and functions
I hope I haven’t confused you even more, good luck with limits!
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