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.

The system works perfectly, it just looks wonky in base 10. In base 3 0.333… looks like 0.1, exactly 0.1

Do you know what an irrational number is?

Sure, let’s do it in base 3. 3 in base 3 is 10, and 3^(-1) is 10^(-1), so:

1/3 in base 10 = 1/10 in base 3
0.3… in base 10 = 0.1 in base 3

Multiply by 3 on both sides:

3 × 0.3… in base 10 = 10 × 0.1 in base 3
0.9… in base 10 = 1 in base 3.

But 1 in base 3 is also 1 in base 10, so:

0.9… in base 10 = 1 in base 10

Carbohydrates are the ones with (H20)n

The word has always had a t sound since Old English, and it’s part of the reconstructed language Proto-Germanic in the form *ufta. Every other Germanic language displays a t in the corresponding word:

Scots oftin (“often”), North Frisian oftem (“often”), Saterland Frisian oafte (“often”), German oft (“often”), Pennsylvania German oft (“often”), Danish ofte (“often”), Norwegian Bokmål ofte (“often”), Norwegian Nynorsk ofte (“often”), Swedish ofta (“often”), and Icelandic oft (“often”).

Source

I really like that description! The study of choice. I think that under that lens I’ll be able to appreciate art in a new way. Thanks.