brokensymmetry
ground state
LMAO
It is absurd to subtract from a given amount and to have no less of an amount than you had before the subtraction.
Numbers are abstract, they don't exist in reality other than as concepts. Now of course, infinity exists as an abstract idea, but when you apply the idea to reality, you get contradictory results. My point is simple.....one cannot POSSESS an infinite number of things (baseball cards, marbles, etc). Nor can one reach infinity as a destination...or....traverse infinity.
To further drive home the point.....I woke up this morning (thank God). Me getting out of bed this morning is an event. Now theoretically speaking, there was an infinite amount of events which led to me getting up this morning...so that "set" in itself is already infinite, not to mention the infinite amount of events that will follow the event of me getting up this morning.
Do you follow? The event of me getting up is a point on the infinite chain, and all the points that preceded this event would make up the infinite set. So the events that followed the event of me getting out of bed would be included on the infinite set that succeeds the event of me getting out of bed.
So pretty much, infinity sliced in half is infinity. Absurd.
That would depend on what you mean, which is why I like real life examples. If by "take away the set of odd numbers", you mean if I was to have the entire set of odd numbers in my possession, and I gave you the entire set of odd numbers in my possession, I would not have any.
Ok, so that is what you meant.
That is the problem!!! First off, you could of used that same example just by giving a scenario of me having an infinite set and giving you the entire set...the answer would still be the same, right?
With infinity, to add or subtract from it is meaningless, because you are not really losing or gaining anything, which is absurd...or how about this...
Take any astronomical number you like....like say 1 to the gazillionth power. If you divide that number into infinity, it can be divided into infinity an infinite number of times.....now take a smaller number, the #2, now divide that into infinity...it can be divided into infinity the same number of times as 1 to the gazillionth power.
But no two numbers can be divided into any amount the same number of times. That is more than counter-intuitive...that is flat out absurd.
I need specifics. You like to get specific for everything except the analogy.
I don't know what is so funny about my claim. I typically translate concepts into 'toy problems' if possible.
There isn't anything absurd about the subtraction I did. You keep saying it is absurd. It isn't. If I have the set of all integers, and I take out the odd numbers, I have a set left of the even numbers. It isn't the *same set*, it's precisely what I'd expect. Where is the absurdity? If you have an infinite set of cards, and we labeled them with natural numbers, and I take all the even ones, you simply have a set left with only the ones that happened to be indexed with odd numbers. The answer is NOT the same. The set is quite different! That's all there is to say about that. I don't see the problem.
You slip from (my version of your argument of course) "with out experience of ordinary objects if you take some away the cardinality of the set is less!" to "therefore this set subtraction stuff is nonsense! can't represent reality!" Well, how do we know that? It is *counter intuitive* but it is a long way from showing that because it is counter intuitive it is literally impossible. Quantum mechanics seems absurd in that sense, being counter intuitive, special relativity even, but we know those things are true about the world. Show me *why* it is impossible to be true in the 'real world' even though it is counter intuitive?
Take the infinite set of all integers. Now, divide the set into two, so you have one that contains all the numbers from 0 and greater and the other one contains all numbers less than zero. You have *2 different sets* now. They are NOT the same! You keep claiming you get the same answer but you don't. You didn't in the case of the odds and evens, and you don't here. I can't help but think you are confusing the cardinalilty of sets with the actual contents of the sets themselves. When you look at what is actually happening to the contents of the sets, the mystery, the absurdity, disappears. This is what I mean by being concrete and specific.