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.
Thanks for your reply!
I hate having to cater to the lowest common denominator, I had to struggle with un-engaging classes all throughout elementary and middle school. I've seriously thought about becoming a teacher so I'd like to ask, in your experience, what happens to the children that are able to process more advanced information? Can something be done to keep them engaged and nurture their development too?
Edited an unfortunate typo
Commenting to check later.
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
Conformal Field Theory?
I instantly thought of Eres Todo para Mí by Nostra Morte
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”).
Colombia*