I have ready about 10 posts that are similar and none of them seem to answer my question so any help is appreciated.
My question is how to miners technically determine if a "wallets" has the "balance" to complete the transaction. Before you say this is a duplicate let me elaborate:
User A has private key A and Public key A.1 and A.2 User B has private key B and Public key B.1 and B.2
Transaction 1 A-> B.1 by User B sending B.1 to A and A signs the transaction (0.5 BTC for illustration) with that private Key. Transaction 2 A-> B.2 by user B sending B.2 to A and A signs the transaction (0.5 BTC) with that same private key.
Now private Key B has 1 BTC. But sense No one knows that B.1 a and B.2 belong to B because those are derived dynamically from B how can you know how much A has? Further suppose you loose track of you public keys, so B.1 and B.2 have been forgotten. How are you able to figure out the bitcoins that B has access to?