# Is an infinite tape alphabet for TM valid? [duplicate]

Can I use an infinite alphabet for the tape in a turing machine?

e.g. with input string as (1, 0)* can I define the symbol 1j as the symbol 1 with j marks on top of it where j in a natural number, to be used on the tape?

2. Such a machine can decide any language over $\{0,1\}$ (exercise).