Couldn't the following simple way be more effective? 1) The set of real numbers is uncountable. 2) Humans can only identify countably many words. 3) Humans cannot distinguish what they cannot identify. 4) Humans cannot well-order what they cannot distinguish. 5) The real numbers can be well-ordered. 6) If this is true, then there must be a being with higher capacities than any human. QED
The appending discussion is not electrifying for mathematicians. But a similar question had been asked by I K Rus in MathOverflow. There the following more educationel discussion occured (unfortunately it no longer accessible there).
(3) breaks down, because although I can't identify (i.e. literally "list") every real number between 0 and 1, if I am given any two real numbers in that interval then I can distinguish them. - C GERIG
If you are given two numbers, then both can be given, i.e., belong to the countable set of finite expressions. - I K RUS
I voted down to close as "subjective and argumentative". Claiming that the well-ordering axiom implies that someone can order the reals is really inane, in my opinion. - ANGELO
I agree. It is really inane. But most mathematicians don't even know that this belief is inane. We should teach them: It is really inane to believe that all real numbers "exist" unless God has a list of them. - I K RUS
God is not the subject of proof. Either you believe or not, but this is only a matter of faith. It would be too simple if a proof of existence or non-existence existed. We should not have any choice. D SERRE
God is the subject of Gödel's proof. God is the subject of my proof. And I am very proud that I have devised a proof that can be understood by a cobblers apprentice (as Euler requested). That will pave my way into the paradise. We know: without God there is no paradise, not even Hilbert's. You rightfully remark, "we should not have any choice." And we have no choice - unless we have the axiom of choice. Now I will no longer respond to questions and comments and will withdraw into my hermitage. Bless you God. - I K RUS
Although I agree with the closing of your question, thanks for bringing up that webpage - it is interesting and useful. @folks - knowledge can come from many sources :) - F GOLDBERG
Yes that's certainly true, but unfortunately in MathOverflow it seems not always appreciated. This instructive question and discussion have been closed as spam and deleted immediately.