Nah not anymore, now you spend a day or so building some convoluted excel calculator once so that you never need to do the calcs again.
Then, 3 years later when you go to add or change something in that calculator, you have absolutely no idea how it works and decide the change wasn't that important anyway.
+ is a map from N×N to N where a + 0 = a and a + S(b) = S(a + b) (S is the successor function that gives the next number).
Then 1 + 1 = 1 + S(0) = S(1 + 0) = S(1) = 2.
No, it's correct. You define the operation by it's properties. It's not saying that "a plus 0 = a" but "the result of applying the binary operation '+' to any number with 0 should give the original number."
is just a symbol. You could instead write it as +(a,0)=a and +(a,S(b))=S(+(a,b)).
You have to have previously defined 1=S(0), 2=S(1), 3=S(2), and so on.
I really recommend the YouTube channel "Another Roof". His first few videos were building up exactly this idea, as well as building up all the real numbers (possibly complex too if I'm remembering correctly). Sounds like a dry topic but he uses humour really well throughout. https://youtube.com/@anotherroof
Engineer: 2, but 3 to be safe.
The budget is for 1.5, make it work.
Oh, hi Boeing Manager.
Was going to say: 2ish
Wouldn't they just look up the answer in a table?
Nah not anymore, now you spend a day or so building some convoluted excel calculator once so that you never need to do the calcs again.
Then, 3 years later when you go to add or change something in that calculator, you have absolutely no idea how it works and decide the change wasn't that important anyway.
programmer: "11"
It's not 10?
Also, oh God, I got yours as I was typing.
confluence of base-2 jokes and javascript jokes...
could have been worse, I could have said `
Am I misunderstanding? '1' + '1', 49+49 = 'b'
I can't math.
Onety one
concat: "11"
cat: ignores your inquiry
No that's "1" + "1"
True
Looks Good To Me!
1+1=3 in cases of large 1's
ok, I define 1 as {∅} and 2 as {∅, {∅}}
proving the addition holds is slightly more complicated
Now define "+"
I love the comment that it's "occasionally useful"
Hmm yes.. set theory... I don't understand anything happening here
There is actually a really good explanation for us math-curious non-mathematicians here:
https://blog.plover.com/math/PM.html
That's some good read, thank you so much.
+is a map fromN×NtoNwherea + 0 = aanda + S(b) = S(a + b)(Sis the successor function that gives the next number).Then
1 + 1 = 1 + S(0) = S(1 + 0) = S(1) = 2.seems a little sus to use + to define +
No, it's correct. You define the operation by it's properties. It's not saying that "a plus 0 = a" but "the result of applying the binary operation '+' to any number with 0 should give the original number."
You have to have previously defined 1=S(0), 2=S(1), 3=S(2), and so on.
I really recommend the YouTube channel "Another Roof". His first few videos were building up exactly this idea, as well as building up all the real numbers (possibly complex too if I'm remembering correctly). Sounds like a dry topic but he uses humour really well throughout. https://youtube.com/@anotherroof
Here is a playlist of the topic: https://youtube.com/playlist?list=PLsdeQ7TnWVm_EQG1rmb34ZBYe5ohrkL3t
ooh, that looks interesting!
1 + 1 is not equal to a question mark.
What did 1 minus 1 equal before zero was invented? 🤔
Yeah, define "zero".
The one invented on India at around the Middle Age is a different one. The one you are asking about is very old.
You forgot accountant
"What do you need it to be?"
We need to report negative earnings so we don't have to pay taxes obviously
Computer Scientist: 10
O(1)
I'm surprised the 6 year old knows factorials.
Not only that, it is mathematically correct, at least given the usual definitions of 1, 2, +, and !
1 + 1 = 2 * 0.999...
Error, float detected when int expected
You can't put an expression on the left-hand-side of the assignment operator.
You need more expressive languages.
Computer Scientist: 0 and a carry bit
Mathematician: S(1)
Quantum physicist: Whats the uncertainty?!
Terrence Howard : 2 !! Also 1x1=2 !!
Math isn't induction. Its deductive logic.
How would a two year old know factorials?
Appliance salesperson: oven + pan = hamburger
I appreciate the latex-style quotes around the mathematician's 1
new captha alert 1 + 1 = 2 to enter
What's great is the kid is correct even with the factorial
How old this be inductive reasoning?
Surely the philosopher is the one looking for definitions..