^_^ thank you!

I like how compact this one is ;)

Not quite. The wording “equivalence classes of … with respect to the relation R: aRb <==> lim( a_n - b_n) as ->inf” is key.

https://en.wikipedia.org/wiki/Equivalence_class

loosely, an equivalence relation is a relation between things in a set that behaves the way we want an equal sign to

For an element in a set, a, the equivalence class of a is the set of all things in the larger set that are equivalent to a.

No. 0.99 is 0.9+0.09. The proof I gave shows that 0.99999999999999999999999999999999999(…) is equal to 1.

and wants to know why 0.999… = 1

\begin{align} 0.999… &= 9\cdot(0.1+0.01+0.001+… ) \ &= 9\cdot( 0.1^1 + 0.1^2 + 0.1^3 + … ) \ &= 9\cdot(\sum\limits_{i=1}^\infty ( \frac{1}{10^i} ) ) \ &= 9\cdot(\sum\limits_{i=0}^\infty ( \frac{1}{10^{(i+1)}}))\ &= 9\cdot(\sum\limits_{i=0}^\infty \frac{1}{10}*(\frac{1}{10^i})) \ &= \frac{9}{10}\cdot (\sum\limits_{i=0}^\infty (\frac{1}{10^i})) \ &= \frac{9}{10}\cdot \frac{1}{(1-(\frac{1}{10}))}\ &= \frac{9}{10}\cdot \frac{10}{9} = 1 \end{align}

The crux rests on a handy result on from calculus: the sum of an infinite geometric series looks likes s = 1/(1-r), when s = \sum\limits_k=0^inf r^k, and |r| < 1.

Sorry for the latex. When will hexbear render latex? This is a bit more readable:

What are your top 2?

Idk. I make a different bean chili in the pressure cooker every week with whatever veggies I can get and whatever variety of beans we have on hand (which is usually a lot because I’m fortunate enough to live in a place with an absurd variety of plant agriculture). We vary the profile of the chili between a few indian-ish seasoning mixtures, this tasty african mixture with a ton of cumin and ras-al hanout, mexican-ish spices, and a few other blends. I use this to make a lot of burritos and tacos. Occasionally we’ll mix them into patties but that’s a huge chore. When my partner or I feel bored with these, we pick a place on a map and try to learn a recipe or two from there and then mix a chili with that dish’s flavors.

Aside from the chili, we’ve been making a lot of indian recipes:

this shit is amazing, but it’s a rare treat for me:

Insects also have brains. Some arachnids have the capacity for fairly complex cognition (e.g., the portia spider’s hunting behaviors, jumping spiders communicate with eachother and in my opinion, engage in playful behavior).

The issue isn’t with your terminology, but rather with what it reveals about the imprecision/inconsistency of your reasoning on these matters.

If you’re going to draw a line at eating beings that can feel the harm done to them by eating, it might serve you to explore that boundary more thoroughly.

yeah the common granulated sugar at the grocery store is usually bleached and mixed with bone char

the most fucked up thing about this in the USA is that they’re allowed to call the ingredient “natural carbon” when it’s used in a situation where it’s required to be listed

So I see no substantial moral difference between eating plants or invertebrates, for example - neither can feel harm.

octopodes have capacity to feel pain and likely experience emotion

https://www.youtube.com/watch?v=V6K1kVUct24

it does get boring pretty quick when it’s just chickpeas and beans as the base of everything.

skill issue

There are so many fabaceae that can be prepared in such a variety of ways that this should appear constructively absurd.

Another way to see it: “it does get boring pretty quick when it’s just chicken and beef as the base of everything”

bees can consent

elaborate

While ER visits for COVID increased 14.7% in the past week nationally, they still only account for 0.7% of ER visits, according to CDC.

How long has it been since hospitals were required to report covid cases/admissions?

I don’t believe killing animals is fundamentally wrong.

When is it wrong to kill a (non-human) animal? When is it wrong to kill a human?

I make a point to bully carnists when they’re overly smug about it.

Do you ever bully yourself?

Anyways, shit was easy

This was my experience as well and I find it really interesting how most people I talk to seem to proclaim the opposite.

any grad student should be able to explain their research in broad layperson terms

100%. I just think caution is warranted for certain cases where a small amount of detail and the year of graduation might be enough to personally identify someone.

but I’m curious if the land he’s bought is in more climate resiliant locations.

When you own land everywhere, you don’t really need to discriminate.

forced insemination falls off in Outside the cultures that enjoy its consumption

This is simply false cw: forced insemination of cows in the indian dairy industry

Look it up instead of arguing with me?

First, I actually did look it up. Second, why didn’t you?

A person online who was only interested in vegan food choices and not a discussion about dairy practices in the west?

lmao YOU asked why vegans don’t eat dairy!

If it’s niche enough, answering this might be very poor opsec

First, at the risk of being a pedant, bickering and arguing are distinct activities. Second, I didn’t imply llm’s results are inherently incorrect. However, it is undeniable that they sometimes make shit up. Thus without other information from a more trustworthy source, an LLM’s outputs can’t be trusted.

Do you really not see why I asked my rhetorical question or do you just want to bicker?