Google still depends on Yahoo! Huh!

NFD Theorem
Google is not independent.

Proof
Here we'll apply the indirect proof(also known as Proof by contradiction) informally.

For convenience, first assume that --

Google is independent. Totally independent. It doesn't use any service from nth party.(where n equals 3) ... ... (a)

Now it will be sufficient to proof this theorem if we can show that at least one third-party service is used in Google website.

We can consider the index page of Google Press Center. There exists a subscription offer(at the left-bottom side) so that people, any people can get updated news about that company via email. Note that the official mailing list of Google Press is hosted byYahoo! Groups.

We get the same return from Google-Friends Newsletter service.

Now we know, all the email addresses subscribed to Google Newsletter are verified by Yahoo Groups.

Again, we know that

Yahoo! Groups is a service of Yahoo company. ... ...(b)
Yahoo and Google are different companies. ... ...(c)

It is clear from equation (b) and (c) that Yahoo Groups is not a service of Google, which contradict to our previous assumption.

Hence the only possibility, Google is dependent on third party service.
(Proved)

Corollary
# Google still depends on Yahoo, it's major rival.
# Google can't rely on their Google Groups 2 Beta which offers similar but better service to yahoo groups.
# Ishtiaque is very intelligent.


Geometrical Interpretation
Before:

After: