And, as a mathematician who has been coding a library to create scaled geometric graphics for his paper, I hate -0.0.
Seriously, I run every number where sign determines action through a function I call "fix_zero" just because tiny tiny rounding errors pile up in floats, even is numpy.
I think we don't give gradual acclimatisation enough credit here. Most of my students have never heard of Firefox and tools like ublock origin because they're acclimatised to the mobile ecosystem
"How do I install something? I use the app store."
"Oh, but I already have the internet on my phone, why would I want a 3rd party app to use the internet" (think old people who mix up AOL with the internet in reverse!)
As soon as I show them, they convert in seconds - they've forgotten web pages without adverts can exist.
I mean, here is a thought, if an AI tool uses creative commons data, then it's derivatives fall under creative commons. I.e. stop charging for AI tools and people will stop complaining.
I'm arguing from the standpoint that we establish the idea of counting using the naturals - it's countable if it maps to the naturals, thus the link. Apologies for the lack of clarity.
On the contrary - to be countabley infinite is generally assumed to mean there exists a 1-1 correspondence with N. Though, I freely admit that another set could be used if you assumed it more primitive.
I teach - I have to debate my basic human rights every day (sleep and time spent not working are apparently not rights I hold according to our more entitled students/managers).
When you count upwards you start from 1, and go up. However, when you count down you usually end on 0. Surely this means 0 satisfies the definition.
The natural numbers are derived, according to Brouwer, from our intuition of time of time by the way. From this notion, 0 is no strange idea since it marks the moment our intuition first begins _
I suppose it's similar to the discussion older and more successful men have about avoiding "gold diggers", "bear traps", and "black widows". Not all women are after a man's money, but those that are will actively seek out such men, so you'll never be safe. One wrong move and you're suddenly working overtime the rest of your life to pay child support for a child conceived without your consent. Whereas, a bear would only run into us by chance, and would be more likely to leave us alone if we dropped our food and calmly walked away.
Edited note for clarity and posterity: Stereotypes are always hilariously offensive - I think some people just learned that.
Huh, neat. Not what I was expecting.
Good short!