By assigning a person to a decimal value and implying that every decimal has an assigned person the meme is essentially counting all the decimals. This is impossible, the decimals are an uncountable infinity. It’s like saying. Would you rather the number of people the trolley hits to be 7 or be dog.
What the meme has done is define the decimals to be a countable infinity bigger than another countable infinity. They’re both the same infinity.
Ah I see why they worded it the way they did. I would argue that’s just the limitation of the illustration, considering the text words the premise correctly, but fair!
But you actually can assign a unique person to every number, you just need an infinite number of people. You literally mathematically can’t do that for uncountable infinities.
Really? Isn’t the point that when you assign a natural number to every real number you can always generate a “new” real number you haven’t “counted” yet, meaning the set of real numbers is larger which is also is the point of the image.
No, thats not what I mean and that’s not the case. Even though there are infinite natural numbers, you can count them all. More accurately you can define a process that eventually will count them all. This is entirely different from decimal numbers which there is no process you can define that will exhaust all decimals. In this way the decimals are uncountable.
When talking about infinities this makes the infinity that contains all decimals larger than the infinity that contains only whole numbers.
My disagreement with the meme is that assigning an individual to each decimal is essentially a process of counting and this is a fundamental contradiction. As such the comparison to the set of natural numbers is nonsensical and the implication that there are less people assigned to the smaller infinity is incoherent.
There are more reals than naturals, they do not match up 1 to 1, for exactly the reason you mentioned. Maybe you misread the meme?
By assigning a person to a decimal value and implying that every decimal has an assigned person the meme is essentially counting all the decimals. This is impossible, the decimals are an uncountable infinity. It’s like saying. Would you rather the number of people the trolley hits to be 7 or be dog.
What the meme has done is define the decimals to be a countable infinity bigger than another countable infinity. They’re both the same infinity.
Yeah, but if you can line up the elements of a set as shown in the bottom track, then they’re, at most, aleph 0.
I don’t think we should take the visuals of the hypothetical shit post literally.
If they say there’s one guy for every real number, let them
Ah I see why they worded it the way they did. I would argue that’s just the limitation of the illustration, considering the text words the premise correctly, but fair!
One person for every decimal isn’t possible even with infinite people. That is the point I’m making.
Neither is assigning a person to every natural number, so I’m not sure what point you’re trying to make?
But you actually can assign a unique person to every number, you just need an infinite number of people. You literally mathematically can’t do that for uncountable infinities.
Really? Isn’t the point that when you assign a natural number to every real number you can always generate a “new” real number you haven’t “counted” yet, meaning the set of real numbers is larger which is also is the point of the image.
No, thats not what I mean and that’s not the case. Even though there are infinite natural numbers, you can count them all. More accurately you can define a process that eventually will count them all. This is entirely different from decimal numbers which there is no process you can define that will exhaust all decimals. In this way the decimals are uncountable.
When talking about infinities this makes the infinity that contains all decimals larger than the infinity that contains only whole numbers.
My disagreement with the meme is that assigning an individual to each decimal is essentially a process of counting and this is a fundamental contradiction. As such the comparison to the set of natural numbers is nonsensical and the implication that there are less people assigned to the smaller infinity is incoherent.
It’s just an illustration… how else would you draw it?
My argument applies to the text of the post too. You literally can’t assign people (count) the decimals.
Diagonally