On Thursday, December 5, 2013 2:35:58 PM UTC-7, WM wrote: > > If you insist that the irrational antidiagonal differs from every entry of the list, you must use a digit d_oo, because up to every d_n it does not differ. >
d only has digits in finite places, one for each Natural Number.
And, no, up to every digit it does Not differ from all entries. But, for Any entry, there is a digit at which it does differ. Hence, d differs from All entries,
It's Not Equal to Any, so it's Unequal to All.
And yes, the qualifier switches when taking the negation.
> If you don't say so, you must agree that an irrational number cannot be defined by its digits but only by a formula supplying every digit. >
I need to agree with what logically follows from my premises.
Also, what the difference btween "defined by digits" and "a formula supplying every digit"?
Doesn't supplying mean defining? Or do you have special definition for that?