a) it is absolutely conceivable to write a cheque to yourself. For example, to move cash between bank accounts

b) the bank has a big database and a system of clearing cheques that ensures you cannot double-spend money by writing yourself a cheque. If you try to kite cheques by abusing the latency in the system they notice because it turns out you can just write that down in a central database too and it's pretty effective

I remember a friend doing that. More funny a friend wrote I owe you $5 and deposited and took out $10 the minimum allowed.

What happened was that person lost the ability to deposit and withdraw.

There is a level of trust but things will catch up to you.

For those that aren't following along, the answer is nothing and the parents comment completely misses the point of being able to attribute something to a person.