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With thinks like cash in banks, you can go to bank office and withdraw your cash. Banks can not refuse your withdrawals because they don't have Internet connection at the moment.
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No you can't. Banks do not have local copies of your account records and without said records they cannot access your accounts so - no withdrawals are possible.
As others have already said, if the entire internet goes down the immediate effects on Bitcoin will be nothing in comparison to what happens to a myriad of essential services.
Exactly! Without the Internet, everything would go down.
Medical records are kept online. Nowadays when you get admitted to a hospital they have everything like your blood type, disease history, recent body mass, height, last prescriptions... Without the network they have nothing. They have to do all the tests and don't even know if you're insured.
Banks have no information about your accounts.
The police won't know if the car you have is yours, if you have driving license... You can carry everything in your pocket but people usually don't. In the EU we don't need any documents because everything is in your personal ID number. You just give that to the police, or your doctor and they can access all your personal files.
Yes, the Internet can temporarily go down due to a virus or a strong EMP, but most people would not care about bitcoin at that point.