Recent content by Sissoev

Don't worry, no offence taken, pwsnafu :smile: I didn't question the axiom of infinity, but the way we deal with it. I think that the "concrete" example clarified my point.

I'm not trying to change mathematics, neither am I challenging your knowledge to prove you wrong. Don't get frustrated if you cannot answer some of my questions and logical points. Most probably that is because my points are so lame that you cannot make sense of them :-p But still, if the...

Let me add to the above hoping that it'll show my point in more understandable way. A pair has a property which should not be confused with the properties of its parts. My opinion is that we should think of pair's property as of the result from 1 liter of water paired with 1 kg of cement. So, if...

Properties of paired sets I see paradoxes as broken logic which occurs by mixing two different properties. Zeno's paradox is a result from mixing time with distance, not taking in account the speed. Hilbert's paradox is a result from mixing pairs with pair parts. Left and right as parts of one...

Thanks Mark! Very good explanation. Now, I understand that the result of infinity minus any number is still infinity, but I still cannot wrap my mind around subtracting from paired sets. Although infinity as number has infinite value, when paired it's bound to the other side as equal value...

OK, I understand and thank you all :approve: Now my question is: Why Hilbert didn't give the simplest answer; unpair the set, add as much as you want and pair it again?

I understand, Mark, but in the example I gave you, I mapped the rooms with the guests in front of them, and we still had one empty room. You'll tell me to move the guests one room back, in order to fix the infinity, but I'll say NO, I've already mapped them and I have one extra room. Who is...

Hahaha :smile: No, Shredder, my claim is that two infinite sets can be paired only once, because if you try to do second pairing, you'll fall into paradoxes like rooms appearing from nowhere and breaking the infinity. How about, emptying all the odd number rooms? We'll get infinite occupied...

Come on, guys! I know that there is no last room in an infinity set, but you don't read carefully. Both the rooms and the guests are infinite as a pairs. Once you take the guests out of the rooms, and try to pair them again, you loose the infinity, and that's why it is wrong to do it. The...

Sure, but that wouldn't make the set infinite again. That would just make the last room empty ;)

Lets keep it simple for you, pwsnafu; imagine that two guests came in the hotel and in order to accommodate them the manager orders all guests to get out of their rooms and move in front of the room with two numbers up. Then №1 moves in front of room №3, #2 in front of room №4 and so on. Then...

To break infinity... :shy: Well, not exactly to break it, but in a meaning that it wasn't infinity in a first place. We know that infinity+1=infinity, but that's not the case with pairs, I think. Why? In the OP I said: In other words; if we pair two infinite sets, and we are left with one...

Can we think of Hilbert's Grand Hotel problem as of infinite number of pairs; room/guest pairs? If we pair infinite number of left shoes with infinite number of right shoes, we will have infinite number of shoe pairs. In such pairing there will not be left any unpaired shoes, because that...