One of the first things that people look at on your twitter profile is your url. The reason behind this is that people naturally want to connect and a profile link gives viewers another place to connect. If you are following people like you should, then most of those same people will come look at your twitter page and want to find out more about you. And hopefully that means they will look at the URL that you give for them to view on your twitter page.
The other part of giving a link on twitter is to send out your preferred link in a tweet. You should use a tweet shortener when doing this. Some great tweet shorteners are bit.ly, ow.ly by hootsuite, and tiny url. There are many link shorteners out there, but these seem to be the most commonly used.
Another good post. As a techno-dummy, I have not known HOW to go about shortening a link using one of the options you gave. I think you just solved that for me my sending me to the sites. Thanks.
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Cool man. Most Twitter apps on your phone have a link shortener built in so u don't have to visit those sites from your phone. Pretty cool