This is part of a series on common misconceptions.
Is this true or false?
Why some people say it's true: Adding one to any number always makes it bigger.
Why some people say it's false: Infinity is not a real number, so this arithmetic is not valid. Also, according to the infinity rules, , with is any real number. Hence,
The statement is .
We cannot do ANY ARITHMETIC OPERATION with infinity, since it is a concept, not a number.
But let's take a look at the limit to prove it is wrong.
Hence, the statement is .
Rebuttal: But what if you have a very large number, say, , will it be larger than infinity?
Reply: You may want to see Is ?
Rebuttal: If you cannot do any arithmetic operation with infinity, what does mean in your proof?
That means you use the one of the properties of infinity to evaluate the limit of a function.