Names and Logos

The first step in registering a business is providing a business name. I believe this is unfortunate, since it forces a marketing decision very early in the process. It is also not very useful for the government since it is the address and legal representative that counts. This is what I treat as my real company name:

Unfortunately, the IRS (as well as other government agencies), do not recognize characters beyond A - Z, a hyphen, decimal numbers, and the ampersand. So, legally, I have to go by "Z to Z Technologies" when I really want to go by "ℤ→ℤ Technologies". (For those curious, ℤ = Unicode 2124 and → = Unicode 2192.)

Why ℤ→ℤ Technologies? ℤ is the symbol for the set of integers, so speaking mathematically, the company is about mapping the set of integers to the set of integers which is (depending on your model of computation), equivalent to saying the company is in the computation business. Philosophically, I've been heavily influenced by the theory of computation and the study of formal languages, so I've had a personal attachment to the meaning behind ℤ→ℤ ever since my professor wrote it on the blackboard.