I for example own 10 BTC does that mean, in some Blocks in the valid part of the blockchain is written, that I received at some point in time a certain amount of BTC? How do I prove that the Transactions in this block belong to me (without loosing ownership).
How hard is it to find all transactions in a chain which belong to me. Some how this should be possible in $\mathcal{O}(l\cdot m\cdot log(n))$ because of the merkle tree in each block for m blocks and l transactions representing my complete ownership (3 BTC + 4 BTC + 3 BTC = 10 BTC)
Could everybody check my amount of bitcoin if he knows my alias or whatever is used to mark my transactions as mine.
Could I just spend someone elses coins?
Thank you very much in advance.
PS.: My Plain written math expression was displayed wrong so I edited as tex code but it still does not work. Anyone who can read tex will still be able to read this formula (probably better than before) If sb knows how to fix it, plz provide a solution.