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Infinity is not a number
As infinity is not a number, you must take care of this in calculations.
Explanation
The calculation of
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is wrong, the correct result is the number e = 2.7182…. Where does the error occur? We repeat the calculation, and look what happens
and so we write
Apparently ∞ + 1 is a little bit more than ∞. That would be an explanation for it. However,
So it is not the proper way. Let us first use usual numbers. We're quite sure, that
is correct, and the result is accurate to 1 decimal place. If we take 1.000.000 the result will become more accurate. You can continue with bigger numbers, the number of decimals will increase and this never stops. Why did it go wrong with infinity? Well, it shows that infinity is not a number. The mistake happend at the very beginning. The calculation should be written like
as it concerns a limit. You should not use brackets in that way. But there was one more error, as
is incorrect. Infinity divided by infinity is undefined. Yes, here you clearly see that infinity is not a number, and that you must apply different calculation rules.