fastest way to print a lot of pdf files 7138

Of course they do! I feel like the argument is going in circles! READ THE UNDERLINED STATEMENT OF THE SITUATION (which you snipped)..

Absolutely. Note "created" and "related" and "infinite" as words in your statement that have respectively connotations of construction, procedure, and beyond-reach-of-construction-or-procedure buttociated with them, and you will begin to see a problem.

He does. That's WHY he says "show me your bijection". Your "bijection" is a function, and functions are defined by computational procedures (I don't believe, for the sake of this argument, in the existence of functions which are not computable, and I don't believe in existence without a witness to the existence).

Please stop trying to teach sucking eggs to grandmothers. This is a perfectly consistent mathematical view of the universe - the cnstructivist logician's universe. Throwing in the word "mathematics" as though it added something to your armoury won't win you anything.

The constructivist universe is a little large than the finitist's universe, and a little smaller than the intuitionist's universe. While the constructivist rejects any notion of function that does not involve computation and any notion of a "completed" infinity (seeing infinite as just a description of an ongoing process without a stop), the intutionist accepts that the concept of infinite and such things is discussable, but refuses to reason about them using an intuition developed for finite objects. In particular, the intuitionist would ask you HOW you choose a representive from a so-called "infinite" set, requiring the procedure to be solid, and not resting on reasoning using for example the logic of excluded-middle (true OR false) to establish your ideas.

Peter