>>4056

>that word "cable" is as archaic as word "chariot"
LOL, that's a good joke. Nonetheless, cable tv and DSL can both be delivered by optical fibre or by copper cable. But they are different technics. The first is a shared medium, the second is an exclusive medium - at least theoretical. If you look from a greater distance, all ways of transmitting are more or less shared.

>at least some of them should be already sharing the same IP
At one time each IP-address is worldwide unique. The ISPs got each a certain amount of addresses, more specifically address-ranges. From this they assign single addresses to their customers and log this together with start time and duration. Whether after a reconnect the IP-address changes or not depends on the ISP's policy and the law he has to follow.

To identify a client you have to lookup the ISP who is in charge for the IP-address in question. This can be done by browsing the databases of the Internet Assigned Numbers Authority (IANA) leading to the databases of the appropriate Regional Internet Registry (RIR) (roughly covering the continents), the National Internet Registry (NIR) and perhaps a local Internet registry (LIR). Or you simply use one or more suppliers out of the myriads of WhoIs-services. Up to here the information is publicly available. Altough you now may know approximately the region, you won't come closer, because the ISPs refuse to publish their logs unless you are a LEA or show up with a court order. In this case the records are searched for the address combined with the timestamp(s) - et voilà - the client is found.
BTW, VPN-providers may also log. It is hard to tell, if you can trust their promise not to do so. Thats the reason why they are only the last resort.

For further info you may want to visit the sites of the Internet Corporation for Assigned Names and Numbers (ICANN), which develops the policies and rules, and the Internet Assigned Numbers Authority (IANA), which executes them. Wikipedia might be helpful too.
Some selected URLs to start with:
https://www.icann.org/newcomers
https://www.icann.org/resources/pages/what-2012-02-25-en
http://www.iana.org/about
http://www.iana.org/numbers

>impossible with just IP-addresses, if a single user is on target.
>of course they are possible, no extra parameters are needed, your ip is like your passport.
Right and wrong at the same time ...
It is right for static IP-addresses. It is wrong for dynamic ones. If you cann't force an address change, you got bad luck. Otherwise you reconnect with a new address and go on. You can try TOR or a VPN to hide your real IP-address. Unfortunately most exit notes are known and blocked themself, because of misuse of the services - bad luck again ...
A very last resort would then be open proxies. But this is a science on its own an far to complex for here to explain.