# 康托尔的配对功能0817

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$$c（x + 1，y）-c（x，y + 1）=$$
$$\ binom {x + 1 + y + 1} {2} + x + 1-\左（\ binom {x + y + 1 + 1} {2} + x \右））= \ binom {x + y + 2} {2}-\ binom {x + y + 2} {2} + x-x + 1 = 1$$

$$c（0，x + 1）-c（x，0）=$$
$$\ binom {0 + x + 1 + 1} {2} + 0-\ binom {x + 0 + 1} {2}-x = \ binom {x + 2} {2}-\ binom {x + 1} {2}-x =$$
$$\ frac {（x + 2）！} {2！ x！}-\ frac {（x + 1）！} {2！（x-1）！}-x =$$
$$\ frac {（x + 2）（x + 1）} {2}-\ frac {（x + 1）x} {2}-x = \ frac {{x + 1）\左（（x + 2） -x \ right）} {2}-x = x + 1-x = 1$$