# Help on clarification of a formal statement concerning algorithms running time

I am reading the following in a book on algorithms (Cormen's to be specific):

That is, we are concerned with how the running time of an algorithm increases with the size of the input in the limit, as the size of the input increases without bound.

I can not understand what is the meaning of the phrase: `with the size of the input in the limit`.
What is the limit refering about?

UPDATE:

Please note that at this point in the book (early fundamentals of chapter 2) there has been no formal definition or mention of Big O or other asymptotic notation except a vague reference on Theta notation

Any help?

• That isn't really a formal statement; a formal statement would be essentially big-O notation, with or without the usual notation. Commented Oct 24, 2011 at 16:30
• Yes.I was meaning that the way it is phrased is very formal Commented Oct 24, 2011 at 19:23
• The author got his PhD in CS around the same time you were born. Please forgive him for not being very good at imagining what it is like to not know any math or computer science. I bet he learned calculus before high school. Calculus is all you need here.
– Job
Commented Oct 25, 2011 at 3:38
• I forgive him :-) Commented Oct 25, 2011 at 4:21
• See this link for the explanation of the Infinite Limit en.wikibooks.org/wiki/Calculus/Infinite_Limits Commented Oct 28, 2011 at 10:31

• JB King:OK I will read this, but in this paragraph, the writers have not yet introduced the Big O notation.So since it has not been yet introduced, it confuses me that they use this concept here which is in the chapter `Fundamentals` Commented Oct 24, 2011 at 16:07