I’m sure you can get frozen spring rolls
I’m sure you can get frozen spring rolls
Come and talk to me when you’ve made a Möbius sandwich with a single piece of bread.
Imaginary numbers have the worst name.
I agree, because really all numbers are imaginary. Numbers are also wonderfully useful for describing nature, and it’s amazing how what might start as a quest for completeness and elegance ends up reflecting something about the real world. Each extension on our use of numbers is an augmentation, an extended toolkit to solve different problems, but doesn’t negate anything which went earlier. For example finding the roots of a polynomial often represents a problem where complex solutions aren’t applicable, and “no solution” is the more meaningful result. One kind of mathematics may be bigger and more complete than another, but that doesn’t make it better or more true. It just depends on what you need from it.
The other fields are attempting to describe reality. While Newtonian physics is useful, as an approximation, it’s also quite clearly wrong. You can imagine a universe which follows those rules but it’s not this universe, and that’s why it’s wrong. Mathematics doesn’t care about this universe, so you can pick whatever rules you want. Imaginary numbers are not “more accurate”, they don’t invalidate any previous understanding. They are an imaginary concept with interesting properties. For mathematics, that’s enough.
The answer to that question didn’t change, what changed is how you might interpret the question.
If I asked “what are the REAL roots of x² + 2x + 2” the answer is still “none”. And prior to imaginary numbers being widely used, that is how the question would have been understood.
Mathematics involves making choices about what set of rules we’re working with. If you don’t allow the concept of negative numbers, the equation “x+1=0” has no solution. If you give me an apple, then I have no apples, how many apples did I have before? The question describes an impossible situation, and that’s a perfectly valid way to view it.
Different sets of rules can change what’s possible but don’t invalidate conclusions based on other sets of rules. We just need to specify what set of rules we’re working with.
Jesus is lord.
Cross defeats Jesus.
Cross is lord.
Pfft. Nothing works the way it used to. What’s an old fart to do?
That’s not just a beard. It’s a chin constructed from hair.
It’s a f█n harmonica. The rectangle is part of the brand name. Check out https://www.fnharmonica.com/en
Those are some cute little hands
“These thoughts are too useful to just stay in my head, I’m going out to get some sticky letters so I can spread the message to the world”
Put da cupcakes in da oven. I’ll be back in 10-15 minutes
Who gets the worse end of that? All things considered I’d much rather have a free country to come home to.
Why would you not want to visit a fascist hell-hole where human rights don’t exist, the rule of law has broken down, and you can be abducted, imprisoned without charge or deported at any moment just for the crime of being foreign?
Nah, it’s a dump and pump. You need cash to buy the dip
I guess it just works better when you can tell which character is which
These kids don’t even know when they’ve got it good. I mean, even being in your 40s isn’t that bad
I used to think that if I could have a superpower I’d like to be able to take a big rancid shit at will, but open up a portal so it would arrive in the pants of a person of my choosing. But these days, what’s the point? Most world leaders could be absolutely destroyed by a well timed beer dump, but Trump wouldn’t even notice anything unusual.
I can hear slightly higher frequencies than most, or at least I used to be able to. Back when TVs used cathode ray tubes I’d have problems with the small portable TVs because they would emit an annoying high pitched tone. Even high pitched tones unintentionally mixed into records. The world is designed for people with typical senses.
I know I wasn’t mature enough, but if being well informed, politically conscious and sensible were a prerequisite for voting, we’d be living in a very different world. As far as I’m concerned, this is most likely to change things for the better.