stupid IP question

Hello!
I'm sorry - I know nothing about computers, but I have a dumb question.
Could someone explain to me if two computers, say in a large city, could have the same IP address on different days, if they were using broadband internet?
Or, is it possible an internet service provider could assign a static IP address to ALL computers using its service for a period of a week or so? (As a sort of security measure?)
In fact... I guess I am just confused about IP addresses in general. Does each computer get a *specific* one or can they be assigned to routers etc. without indicating a certain computer?
Thank you!!!

Your assumption is correct.
Because the number of available Internet routed IP addresses is limited
(at least for the time being until someday IPv6 will take over IPv4)
most ISPs have many, many fewer Internet IP address than customers
they have to provide with.
The same is mostly true for the bandwidth they sell.
They speculate that not all their customers will require Internet access at the
same time (much like a bank has more debters than they could redeem instantly).
Therefore they only posses a limited pool of IP addresses that they
assign dynamically each time a customer requests Internet access.
Because of the limited pool and the great demand it happens regularily that the next client in the queue gets the very same IP address someone else have been holding so far once he quits or gets kicked of (which forcebly happens at least once a day even for DSL clients of many ISPs)

hello,

a good IP allocation engineering maybe wont do that. they use the form of NAT and NAT and NAT and NAT again and so on - plus with the help of proxy, and DHCP - so even if you have been allocated with a non private IP addr (or so called a public IP) your real IP still invisible to the internet.

cheers...

It is possible on any type of service that is DHCP driven, whether it be a few people requesting or a thousands.

No. This would not work.

Think of IPs as something that is borrowed whenever anything asks for it.

[NAT*NAT++]+proxy+dhcp is what you're suggesting. IP addresses aren't "invisible to the internet."

It is not regular for an internet service provider's DHCP server to break lease to reassign to another address requesting device due to a shallow allocation. This does not "happen daily " and it doesn't matter what kind of connection.