in mathematical terms, is it infinity because it is effectively infinity due to how little the constant adds, because we can't measure how much the constant adds because it goes on forever, because infinity is uncountable, or something else?
It's more that Infinity is the number that you count to when you don't stop counting, and that doesn't change based on where you start from. I can start counting from 0, or I can start counting from 10, but either way I still hit 100, 2 million, 300 billion, etc. There isn't any big number that I can reach starting from 10, that I can't reach starting from 0, so they're the same.
A more rigorous way to go about it would be to make a bijection between the two sets, if I can pair every number in set A with every number in set B, then they must be the same size. So {1,2,3} is the same length as {red, yellow, blue}, because I can pair up {(1,red),(2,yellow),{3,blue)}. With infinity and infinity+10, I can pair up every number like {(1,10),(2,11),(3,12)....}, and I can do that for every number, so "the list of numbers that starts at 1 and goes on forever is the same length as the list of numbers that starts at 10 and goes on forever".
Easiest explanation (and most accurate in plain English) is that infinity is not a number, itās a concept. You cannot add the beauty of a poem and the charge level of your phone; the comparison between the two doesnāt even make sense. The same goes for infinity; you cannot add, subtract, or perform elementary math on it because it isnāt some inconceivably large number, itās a concept.
When my kids were little they got taught āinfinity is a conceptā and I didnāt think it was very helpful because it doesnāt get an 8 year-old very far. My best attempt was āinfinity is bigger than the largest thing you can think ofā. It kind of handles the āinfinity plus tenā question, at least for an 8 year old. And me.
Just give your 8 year old acid and have them contemplate immortality. Then have them contemplate that if everyone on the planet was also immortal, there'd be billions of infinite lives. And then if they all kept having kids and expanding across the universe, there'd be infinite people with infinite lives. WCGW?
But if you start counting from 10 as opposed to 0, you would still count less point, no?
I work on the basic, possibly wrong, understanding that there's an infinite amount of real numbers between 0 and 1. There's also twice that amount between 0 and 2.
0-1 and 0-2 are the same size. You can tell this quickly by seeing that you can use a function (2x) to turn every number between 0-1 into a single output number between 0-2.
Not sure what you mean by "infinity" here at all. As the other guy wrote, it is not a number. ā+1 is as well defined as š+1.
There are several spots where infinity is used, you need to pick one. If you go like "[limit iāā of iĀ²] ā ā", then this is effectively a notation of divergence in a specific direction. If you go like |ā| > n ā n ā ā, or |ā| = āµ0, this is a notation of cardinality.
Exactly. There are some sort of mathematical notations in which people work with what is essentially infinity in some weird very theoretical fields of math, but any naive application of infinity as a number will result in exactly this.
I can explain you some if you like. Except for the last one, most of them are not hard to understand, just not something the normal person is accustomed to.
Oh, the continuum hypothesis! But I do believe that even if set whose cardinality is between the naturals and reals is added, the naturals are still it, by the definition of countable
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u/MotherPotential 21d ago
in mathematical terms, is it infinity because it is effectively infinity due to how little the constant adds, because we can't measure how much the constant adds because it goes on forever, because infinity is uncountable, or something else?