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I do not understand.
-- Carl Linderholm, Mathematics Made Difficult
Let me explain why it's not easy to see that 5+4 is not 6.
Earlier, the numbers were defined as
2 = 1+1
3 = 1+2
4 = 1+3
5 = 1+4
6 = 1+5
7 = 1+6
8 = 1+7
9 = 1+8.
Where + is associative.
Consider a "clock" with 3 numbers, 1, 2, 3. x+y means "Start at x and advance y hours".
3
2 -> 1
Then 1+1 = 2 and 2+1 = 3, as per our definitions. Also, 3+1 = 1 (since if yo... (read more)