I had a cat once that brought home a barbecued sausage. It was still warm….I’m convinced he stole it off someone’s backyard grill when they weren’t looking. He was a VERY food motivated kitty - former stray who would bolt any food you put in front of him, no matter how recently he’d been fed.
He was also a typical orange cat (one brain cell). Had a call one time from someone a few streets over who begged me to come get him, as he was pawing at her closed glass sliding door, convinced that it was his house. Fortunately she could read his tag with my phone number through the glass (she was allergic to cats). When I went to pick him up, he thought I was taking him away from HIS house, so he was not happy….until he got to his real home, then he trotted happily inside. Sigh, I still miss him and he’s been gone for years.
What an adorable doofus. I had a cat years ago that was much the same with food. She once lunged at and ate raw onion because she was convinced I was keeping her from a tasty treat. The look on her face!
I have a monitor that’s almost like this and it’s surprisingly nice. It feels like a two-monitor setup. Two actual monitors would probably have been cheaper, but I got mine from work, so it wasn’t a factor.
The real advantage of having two actual monitors is being able to flip one vertically for reading code.
I bought one after some months of remote work in 2020. Then when I started my new job they gave me another one (different manufacturer but exact same panel size). I needed to rearrange my desk a lot, but holy shit so much room for error messages!
Yup, virtual machines usually have a really bad drop in performance. “Usually”, because you can reserve a spare graphics card and resources only for use with this one specific machine. But in that case, you might just buy another computer or dual boot (thats what I did while getting used to Linux) instead.
This is correct. The natural numbers are better known as the counting numbers, and do not include 0 or the negative numbers. I personally think the classification is a bit bullshit given how they really only matter in meatspace. I have never seen the distinction between integers and natural numbers come up in real mathematics
Idk if you are trolling, but in most cases 0 is considered a part of the natural numbers. And there is a huge difference between the naturals and the integers: the naturals are for induction, the integers are for algebra.
Depends on where you are! In some places it is more common to say that 0 is natural and in other’s not. Some argue it’s useful to have it N, some, say that it makes more historical and logical sense for 0 not to be in N and use N_0 when including it. It’s not a settled issue, it’s a matter of perspective.
Those are valid points and make some practical sense, but I’ve talked too much with mathematicians about this so let me give you another point of view.
First of all, we do modular arithmetic with integers, not natural numbers, same with all those objects you listed.
On the first point, we are not talking about 0 as a digit but as a number. The main argument against 0 being in N is more a philosophical one. What are we looking at when we study N? What is this set? “The integers starting from 0” seems a bit of a weird definition. Historically, the natural numbers always were the counting numbers, and that doesn’t include 0 because you can’t have 0 apples, so when we talk about N we’re talking about the counting numbers. That’s just the consensus where I’m from, if it’s more practical to include 0 in whatever you are doing, you use N0. Also the axiomatization of N is more natural that way IMO.
You are talking to one right now :) (not sure if a bachelors degree is enough to call yourself one)
you can’t have 0 apples
You can actually. In fact, right at this moment I have 0 apples. If 0 is not natural, then you have no way of describing the number of apples I have.
There are a lot of concepts (degree of a polynomial, dimension of a space, cardinality of a set, in a graph) where 0 is a natural possibility.
So I think 1 indexing is fine, I use it all the time, but to me 0 belongs with the natutals. I will say tho, that 0 does not make sense to me as an ordinal. “He finished the race in 0-th place”???
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