They have to get smaller to fit the problem statement- if all levers are the same size or have some nonzero minimum size then the full set of levers would be countable!
Now we play the game again 🤓. I start by removing the levers in the field/scale of view of your microscope’s default orientation.
But look at the picture: the levers are not all the same size- they get progressively smaller until (I assume from the ellipsis) they become infinitesimally small. If a cluster has this dense side facing you, then you won’t “see” a lever at all. You would only see a uniform sea of gray or whatever color the levers are. You now have to choose where to zoom in to see your first lever.
This reply applies to @Cube6392@beehaw.org’s comment too.
It might sound trivial but it is not! Imagine there is a lever at every point on the real number line; easy enough right? you might pick the lever at 0 as your “first” lever. Now imagine in another cluster I remove all the integer levers. You might say, pick the lever at 0.5. Now I remove all rational levers. You say, pick sqrt(2). Now I remove all algebraic numbers. On and on…
If we keep playing this game, can you keep coming up with which lever to pick indefinitely (as long as I haven’t removed all the levers)? If you think you can, that means you believe in the Axiom of Countable Choice.
Believing the axiom of countable choice is still not sufficient for this meme. Because now there are uncountably many clusters, meaning we can’t simply play the pick-a-lever game step-by-step; you have to pick levers continuously at every instant in time.
It’s an old copypasta from reddit haha. I modified it to add the Fediverse stuff and my complaints with LaTex and improper rotation.
I didn’t actually downvoted your comment but apprently someone did and now I look like an asshole 😢.
I just downvoted your comment.
The amount of points on your comment will be decreased by one. The deduction will be federated across thousands of Lemmy instances, bringing you shame from across the Fediverse.
There are several reasons I may deem a comment to be unworthy of positive or neutral points. These include, but are not limited to:
As this is your first time receiving my downvote, I will provide reasons (listed below) to help you avoid making these mistakes again. Note that this will not be the case with future downvotes.
No - not yet. But you should refrain from making comments like this in the future. Otherwise I will be forced to issue an additional downvote, which may put your commenting and posting privileges in jeopardy.
Sure, mistakes happen. But only in exceedingly rare circumstances will I undo a downvote. If you would like to issue an appeal, shoot me a private message explaining what I got wrong. I tend to respond to PMs within several minutes. Do note, however, that over 99.9% of downvote appeals are rejected, and yours is likely no exception.
Accept the downvote and move on. But learn from this mistake: your behavior will not be tolerated on mander.xyz or the Fediverse as a whole. I will continue to issue downvotes until you improve your conduct. Remember: Posting is privilege, not a right.
Just read the article from MIT. Dont fall for clickbait.
With Newtonian physics if you have two neutron stars orbiting each other they would just continue orbiting forever. With general relativity, the orbiting neutron stars shed energy by sending out gravitational waves. Losing energy they get closer and closer and then merge.
If I give you the entire real line except the point at zero, what will you pick? Whatever you decide on, there will always be a number closer to zero then that.