this post was submitted on 02 Oct 2025
527 points (98.9% liked)
Science Memes
16932 readers
3530 users here now
Welcome to c/science_memes @ Mander.xyz!
A place for majestic STEMLORD peacocking, as well as memes about the realities of working in a lab.
Rules
- Don't throw mud. Behave like an intellectual and remember the human.
- Keep it rooted (on topic).
- No spam.
- Infographics welcome, get schooled.
This is a science community. We use the Dawkins definition of meme.
Research Committee
Other Mander Communities
Science and Research
Biology and Life Sciences
- !abiogenesis@mander.xyz
- !animal-behavior@mander.xyz
- !anthropology@mander.xyz
- !arachnology@mander.xyz
- !balconygardening@slrpnk.net
- !biodiversity@mander.xyz
- !biology@mander.xyz
- !biophysics@mander.xyz
- !botany@mander.xyz
- !ecology@mander.xyz
- !entomology@mander.xyz
- !fermentation@mander.xyz
- !herpetology@mander.xyz
- !houseplants@mander.xyz
- !medicine@mander.xyz
- !microscopy@mander.xyz
- !mycology@mander.xyz
- !nudibranchs@mander.xyz
- !nutrition@mander.xyz
- !palaeoecology@mander.xyz
- !palaeontology@mander.xyz
- !photosynthesis@mander.xyz
- !plantid@mander.xyz
- !plants@mander.xyz
- !reptiles and amphibians@mander.xyz
Physical Sciences
- !astronomy@mander.xyz
- !chemistry@mander.xyz
- !earthscience@mander.xyz
- !geography@mander.xyz
- !geospatial@mander.xyz
- !nuclear@mander.xyz
- !physics@mander.xyz
- !quantum-computing@mander.xyz
- !spectroscopy@mander.xyz
Humanities and Social Sciences
Practical and Applied Sciences
- !exercise-and sports-science@mander.xyz
- !gardening@mander.xyz
- !self sufficiency@mander.xyz
- !soilscience@slrpnk.net
- !terrariums@mander.xyz
- !timelapse@mander.xyz
Memes
Miscellaneous
founded 2 years ago
MODERATORS
you are viewing a single comment's thread
view the rest of the comments
view the rest of the comments
You've misunderstood "some infinities are bigger than others." Both of these infinities are the same size. You can show this since each person on the bottom track can be assigned a person from the top track at 1 to 1 ratio. An example of infinities that are different sizes are all whole numbers and all decimal numbers. You cannot assign a whole number to every decimal number.
Matt parker does a good video on this. I can't remember the exact title but if you search "is infinite $20 notes worth more than infinite $1 notes" you should find it.
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.
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.
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
It's just an illustration... how else would you draw it?
Diagonally
The bottom rail represents the real numbers, which are "every decimal number".
No it's doesn't because the bottom rail is a countable infinity, the decimals are an uncountable infinity. Go watch the video it explains it.
Natural numbers < whole numbers < rational numbers < real numbers
Okay, to clarify, I mean the "is partial set of" instead of "is smaller than".
Your saying it would be correct for "whole numbers" and "decimal numbers". But that's exactly what OP said "natural" and "real"
actually you can show that the naturals, integers and rationals all have the the same size.
for example, to show that there are as many naturals as integers (which you do by making a 1-to-1 mapping (more specifically a bijection, i.e. every natural maps to a unique integer and every integer maps to a unique natural) between them), you can say that every natural, n, maps to (n+1)/2 if it is odd and -n/2 if it is even. so 0 and 1 map to themselves, 2 maps to -1, 3 maps to 2, 4 maps to -2, and so on. this maps every natural number to an integer, and vice-versa. therefore, the cardinality (size) of the naturals and the integers are the same.
you can do something similar for the rationals (if you want to try your hand at proving this yourself, it can be made a lot easier by noting that if you can find a function that maps every natural to a unique rational (an injection), and another function that maps every rational to a unique natural, you can use those construct a bijection between the naturals and rationals. this is called the schröder-bernstein theorem).
it turns out that you cannot do this kind of mapping between the naturals (or any other set of that cardinality) and the reals. i won't recite it here, but cantor's diagonal argument is a quite elegant proof of this fact.
now, this raises a question: is there anything between the naturals (and friends) and the reals? it turns out that we don't actually know. this is called the continuum hypothesis
I clarified my above comment