Math & Mutuals

Sorry if it’s a little cramped- had to make this all fit in ten photos. Hope you guys like it….. and again…. sorry Andrew

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I crocheted a series of hyperbolic planes and strung them up into a garland. Each module is one more round than the one before, and each round has twice the stitches as the round before.

I made eight iterations; the largest one took an entire skein of cotton yarn. I really liked how this shows the change in curvature as cross section of the plane expands.

The other night I had a fever and I was delirious and while I was trying to fall asleep I had some sort of math related epiphany and everything made sense but now that I am not having a fever dream anymore I can’t get back on that train of thought. Disappointing.

Anyways do you think that the difference between 0 and 1 is greater, less, or equal to the difference between 1 and ♾️? I can see it all three ways and I’m curious what other people think. I’ve asked a few people so far, and the answers are varied.

My dad says less, my mom says greater, the engineering professor from UBC (University of British Columbia) I contacted said a lot of things I didn’t understand and I’m still trying to figure out what his conclusion was but I think it was something along the lines of “it depends”. My 7 year old cousin didn’t know what infinity was but once I explained she said less. My cat’s response was too abstract for me to understand but I think he’s leaning towards greater. My 19 year old cousin says they’re the same, if you can consider 0 and infinity to be opposites. During my fever dream, I was leaning very strongly towards greater but I don’t entirely remember why.

It’s an interesting question because there’s so many different types of 0s and ♾️s and so many different ways of thinking about numbers and what 0 actually means and stuff.

Also!!! Please put your reasoning in the notes!!!! I want to see your thought processes!!!

Specifically under: properties: cardinality

We can argue that the amount of numbers between 0 and 1 is „A“

(also this will be in base 10 so an answer can be derived, but base 10 is arbitrary and a different base with equal viability will give a different answer, ergo indeterminacy)

And amount of numbers between 1 and something is „B“

For example:

A={0,0.1,0.2,0.3…0.9,1.0}

B={1.0,2.0,3.0…9.0,10.0}

Now B{[1.0,2.0]} contains all of A.

B/100={.01,.02,.03….09,0.10}

Now the magnitude of a set should not impacted its length:

„If I have 10 items, but they now have a different size, how many items do I have?“

But B/100 is now contained by A{[0.0,0.1]}

We can establish B= an infinite set which contains goes from n=0 to n=set_index of :

10^-(Ceil(set_index+epsilon)/10) •each number of B‘s. infinite set based on n

Where the above has equal length to the set at hand and when multiplied by the 10^ (Ceil(highest possible set index + epsilon)/10) the originally B set will be scene in this magnification.

When we have B zoomed out like this, B becomes a subset of A

.This is arbitrarily recursive, for you could throw this zoomed out B set to be arbitrarily smaller or larger depending on modular system, and arbitrarily smaller or larger than the A set, which means you could choose by what difference any given B set is larger than any given A set (negative meaning smaller than).

This can be done because you are treating infinity like a number rather than a rate, which is why calculus works, but this doesn’t.

Note: these problems arise even if we don’t have B‘s upper bound being infinity, and because you’ve merely said infinity, and it’s undefined in 2 ways that do not cancel eachother out.

So the correct answer is:

He was talking about it in the context of designing robots that would go in and stop nuclear reactor meltdowns, something that would 100% destroy the robot, but they would be designed to keep functioning and fighting the meltdown for as long as possible. He had some designs where over 80% of the robot has died and it was functionally dragging its corpse around by its one working arm because one more minute of functionality might save thousands.