I have a question regarding creating a public address offline, using bitcoin qt and or vanitygen.

How does bitcoin qt and or vanitygen know the public address you created isnt already in use if created offline? And if it is by transferring coins to that in use address you would basically be giving your coins to someone else by mistake.. or cause an anomaly of two of the same addresses in the blockchain.

Math.

This math is above my head, can you please explain?

People have a hard time with big numbers. Bitcoin addresses are 160 bit hashes, meaning that there are 2

^{160} or 1461501637330902918203684832716283019655932542976 possible addresses. Your chance of finding a private key that generates a public key that hashes to the address in my signature is about 1 in 1461501637330902918203684832716283019655932542976.

If you don't care about matching an exact key, but just any other key, the birthday problem says that you need a lot fewer attempts. The approximate number is

*sqrt(2*H*ln(1/(1-p)))* where H is the number of possible addresses and p is the probability you are willing to live with.

If you are willing to take a 1% probability, then you need to try roughly 171464281994822466873809 different keys. That number is 24 digits long, or a bit over 2

^{77}. For comparison, at block # 227663, the amount of work embedded in the hash chain was 899359750187287492752, which is a bit less than 2

^{70}.

So, if you had the enough computing power to do in one year what the entire global bitcoin network did in 4+ years, it would take you about 2

^{7}=128 years to have a 1% chance to find a single address collision. And the odds are really good that you'd find one of your own addresses a second time, not one with money in it.

I'm not checking my numbers very carefully, so I might be somewhat off along the way, but even if I'm off by a lot, you still don't need to worry about it.