Recent content by Mr X

Yes thankyou, it seems really interesting. I'll definitely look more into it. I've went through them all, and explored the best I can with the time I have at my level. This entire discussion was, least to say, fascinating. My question is now answered and I've got some ideas on which direction...

I've read through the further replies, but I'll need some time to fully understand the ideas as well as go through atleast bare minimum of the materials given, so I'll post another reply afterwards. Thanks again.

I think I've got the gist of things, real life was as well as abstract maths vise. Thankyou all for helping out. I'll look into the materials provided and continue by myself later on.

I'm postive a field requires any two binary operators, but I don't know about the construction of real numbers so if you're talking about that specific case, then understood.

I don't quite understand this, but I'll look into it, thankyou

That's.. not quite how that question works. By that logic we should add algebraic properties in properties of triangles, as well as for circles. I'm not sure how to rephrase the question better than I've done, so I'll leave it be here.

It's not about mathematics, it's about properties of real numbers. Not even the real number field, but just real numbers. Ordering and completeness are innate properties of the real numbers, but what about algebraic? They're operators used on real numbers, not a part of real numbers itself. Well...

I've seen a few but most of them simply go to addition and multiplication but never explains why we choose those specific operators. Not even a statement saying that it's for convenience. I'll go through the playlist you've attached as well as soon as I can. Understood. Thankyou Ill get back...

The properties of real numbers are listed as order, completeness and algebraic properties. I can understand order and completeness, atleast i get why it's there but why algebraic? If we consider real numbers as the number line or an infinite set, where does addition and multiplication come in...

My bad, I didn't see the clarification allready posted before posting the other message. And thanks for the heads on which CDA specifically.

That wouldn't solve the real number interval's countability problem, will it? That only shows there exist an uncountable set, which is the powerset of the natural numbers, which can have the same cardinality as the set of infinite binary strings. For this part, which is a specific example, and...

I see. So this theorem is further simplified, or rather used in a different setting that is familiar to introductory course students, and the simplification, in and of itself creates a few misunderstandings and necessitates some inelegant parts which causes the confusion. Which includes the...

Okay, understood.

Yes, got it. But isn't it like bit of an overkill when diagonalisation argument can do the job? Though I hadn't thought about it that way, thanks on the different viewpoint.

I got the gist of it, thankyou, But I didn't fully understand this part. Don't we use the that reals between 0 and 1 are uncountable to show reals are uncountable in the first place? So won't linking it to the countability of reals to (0,1) end up as a cyclical argument? Or are you saying that...