Yay!

I'm done with my thesis! I'm free from "psychological" issues from now on!! Have to indulge myself in maths world!! YEAH!!

Yes, "make sense to others" is not a very reliable test of logic. A day on the Forum will convince you of that!

Yes, there will be a patch like that for me up there!

I found this in my maths textbook talking about logic.

	The reasoning we use as we proceed from what we know to what we wish to show must be logical. It must make sense to others, not just to ourselves.

I couldn't help laughing. Most things in maths do not "make sense" to most people.

This sounds like a real improvement... GOOD WORK!

Another test! I knew all the answers but I did not have enough time to spell them all out. I was so sure of the answer of one question that I forgot I needed to write it down. Uh. I have to train up my speed...

Thanks for the reputation. I learned a hard lesson for what I put down in that post. But I always doubt the usefulness of posting them there...

I've just realized that it should be numerical equivalence rather than denumerability. I must be very tired from my part-time job. Yea that's very beautiful. I still remember the thrill when I was in the algebra lecture. Analysis is less interesting in school's syllabus, but the book you recommended contains a few topics that make the whole thing just very interesting. I just need time to consolidate - make those stuff mine.

It is beautiful, isn't it? Exciting, too. You never know where some familiar idea will pop up next. Mathematics is all about connections like this, and there are very few things discovered in one area that have no application to many others!

Denumerability is another equivalece relation! I'm afraid there are infinitely many equivalence classes for denumerability. I like this kind of wrapping of mathematics. Theories of one level are often applicable to the higher levels. I really want to know how far things can go... Maths won't stop surprising me.

Yes, cardinality is defined in terms of mappings between sets.

Now I know why the set of real numbers and the set of integers do not have the same size. Something to do with functions! Surprise to me!

The 6th is particularly hard to prove. I may have a vague idea on what it's getting on, but both of them have infinite points, and this means I have to make one infinity more than the other infinity, and my brain starts to get messed up at this point. lol No clue.
The factorial zero is a surprise. I should check it out soon.

Yes, those "odd" math facts touch on some deep things that you won't have seen yet.

Time to get a little more confidence in your ability; you can't let "psychology" stop you... be bold and press on!

Ouch. I finally got my time to read your proof in the D-nile question in detail after finishing recruitment of participants for my cog. psy. experiment. I first printed out the part not hidden, and get to the right direction to complete the proof, but rejected it out of useless self-doubt, and later discovered that I was correct after reading what's hidden! And I did exactly the same for several questions in my second math test. I'm going to kill myself.

lol It's alright. I'm still working on the test and I have just successfully solved a problem. I just knew the prof. intended to make things hard for us. I simply need more time to work on the problems. I insist to do everyone on my own!!

I'm sorry... I know it's an awful feeling. I wish I could help.

I failed the test today, very likely. I can only answer half. I know the professor intentionally set up the test this difficult. A lot of people swore after the test, including me. I think I need at least 3 hours to fully answer the whole paper. And again I knew how to do one question RIGHT AFTER I handed in the paper.

Argh @#$%@#$%.