This follows my recent post on this topic.
Maybe, maybe not...
[snip]
>
> Finite linear (over rationals)
> combinations of transcendentals will be transcendental but
> this will keep the set with patterns countable.
>
[snip]
Finite linear combinations of transcendentals MAY be transcendental
but even this statement needs work. The conclusion that the
number of the beasts remains countable will stand.
Suppose T is a transcendental with some pattern.
Then 1 + T is transcendental and has (pretty much) the same pattern.
Clearly 1*( 1+ T) + (-1) * (T) = 1 is a Q-linear combination of
transcendentals which is NOT transcendental.
I think I will go back to sleep. ...Probably more productive!
JT
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