If your ISP provides static IP address service, you can expect your IP address to stay the same even if you disconnect from the Internet and reconnect to it later.
Contrary to popular belief, you do not need a static IP address in order to run a server on your own computer. Dynamic DNS services provide a way to give your computer an Internet hostname that does not change, such as example.is-a-geek.com. These services automatically update the IP address that corresponds to your hostname every time your IP address changes. For more information about dynamic DNS services, see my article how do I get a hostname for my own computer?
Static IP addresses are required only for those who intend to run their own DNS servers. In this case, at least two static IP addresses are required. You will still probably want to pay for another company with a more reliable connection to run your DNS, as this is very inexpensive. See the article how do I host a real domain name at home? for more information.
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