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Yes, both of the transactions was from my own wallets to my own wallets but how can a client detect that? Maybe my wallet was on my android device and completely unlinked with PC (it wasn't in this case), how would the client know it's mine if that happens? In Multbit they were in different wallets, I mean all of those private keys weren't in a single wallet. Each wallet only has a single address (key). I sent from one wallet (with single address) to another wallet (with single address). idk if I'm making sense or not. To put it simple, it wasn't what you're describing, what I did was technically different. It was from my wallet to my other wallet NOT my address to other address.
If anyone can spend unconfirmed transactions then what's the point of getting confirmations? Why do people insist on it? They could just take unconfirmed coins and send them while they're still unconfirmed and they still get there.
Technically speaking there are no wallets, just keys. What you describe is a way the programm you use shows you things, not how they actually are. Did you do this? (or did this happen):
A, B, C refer to public addresses (that allow receiving) and to the coresponding private key (that allows spending)
A holds 1 BTC from 1 input, B holds 0
send A to B (TX1)
before TX1 gets any confirmation send 1 BTC from B to C (TX2)
TX2 should not be possible, because the client has to check whether B has the right to spend 1 BTC. As long as TX1 is not confirmed (single confirmation is enough) B has no right to spend any BTC. It might be that your client allows you to broadcast (!) the transaction anyways, but this makes TX2 invald and it can not confirm until TX1 is confirmed.
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I sent from Multbit on my PC, totally unrelated to blockchain but both the transactions showed up on blockchain.info and both were unconfirmed. Basically it was a new address with two total transactions, one income and one output and both of them were unconfirmed.
Every transaction has to be included in the blockchain. No transaction can be unrelated to the blockchain. The blockchain is where every transaction is storred, it is where it is written that you actually can spend to coins you want to spend.