1 + 1 = ?

[AlbusMalum]

I need some help...
What's one plus one?

[compte obelète]

I need some help...
What's one plus one?

about 3 possibilities:
;2

;11

;glass (fenêtre in french)

[SteveV]

I need some help...
What's one plus one?

10 (binary )

[Woodruff]

I need some help...
What's one plus one?

1,99999... (9 digits to infinity)
Or the same as 1 × 1
Also 2 × i^4

[Phoxtrot]

As long as addition has been properly defined, it's 2.

The proof can be found here:
https://blog.plover.com/math/PM-translation.html

[jacobsldr]

As long as addition has been properly defined, it's 2.

The proof can be found here:
https://blog.plover.com/math/PM-translation.html

This. With the important part being how addition is defined. Must say, when I took Abstract Algebra, this concept that you can have a system where 1 + 1 does not equal 2 (because you may not even have a 2), blew my mind the most.

[robinzig]

Must say, when I took Abstract Algebra, this concept that you can have a system where 1 + 1 does not equal 2 (because you may not even have a 2), blew my mind the most.

Not sure I understand what you mean here. While I can't comment on set-theoretic definitions of 1, 2 and addition, in abstract algebra - specifically in Ring Theory - the concept of 2 only really makes sense if you define it as 1 + 1. In fact, if you allow me to be even more geeky , the fact that the integers are an initial object in the category of rings (see here for explanation) means that there really is no other "sensible" way to define it.

And I don't know what you mean by "you may not even have a 2". You must always have one (at least assuming you have a 1 - not all definitions force rings to have a multiplicative identity, but clearly if you don't have one then the statement "1 + 1 = 2" doesn't make any sense), and as I just said it must be defined as 1 + 1. Note that the integers modulo 2 do NOT form an exception, if that's what you're thinking of - while it is true there that 1 + 1 = 0, you also have that 2 = 0 so there is no contradiction.

PS kudos to the OP, I thought it was meaningless trollery but it's given rise to some interesting replies!

[jacobsldr]

Well, I can easily not have a 2 in a system of my own definition. The OP put no limit on what system they wanted by ending the equation with a question mark.

Can't I have a Field that only contains the set (0,1) would like set symbols here instead of parenthesis.

Then, 0+0=0, 0+1=1, 1+0=1, and 1+1=0 also 0*0=0, 0*1=0, 1*0=0, 1*1=1

No 2 needed.

Now, I am shooting from the hip here because not sure even where my book or notes are from that class, it has been awhile (and was for sure the subject in math i struggled with, Calculus was my thing), so feel free to crush this thought as i do enjoy this type of discussion

[robinzig]

Well, I can easily not have a 2 in a system of my own definition. The OP put no limit on what system they wanted by ending the equation with a question mark.

Can't I have a Field that only contains the set (0,1) would like set symbols here instead of parenthesis.

Then, 0+0=0, 0+1=1, 1+0=1, and 1+1=0 also 0*0=0, 0*1=0, 1*0=0, 1*1=1

No 2 needed.

Now, I am shooting from the hip here because not sure even where my book or notes are from that class, it has been awhile (and was for sure the subject in math i struggled with, Calculus was my thing), so feel free to crush this thought as i do enjoy this type of discussion

Not going to "crush" it because you're not wrong, as such - you can certainly have a field with 2 elements. That's just the integers modulo 2 where, as I said, 1 + 1 = 0 but then we still have 1 + 1 = 2 because 2 = 0. (Strictly speaking "2" and "0" here represent equivalence classes of integers under the equivalence relation defined by having the same remainder on division by 2 - so there are only 2 equivalence classes, that of even integers and that of odd integers, and 0 and 2 of course belong to the same one.)

[voriki]

1 + 1 = 3 with a 9 month wait period.