自然数の演算(2)
「数学とソフトウェアのページ」の「自然数の演算」の操作の例の続きです。
を示します。
他にも
が成り立つのですが、これを示すには機能が不足しているかもしれません。
(2-1) ![(a + b)^\wedge = a + b^\wedge](https://chart.apis.google.com/chart?cht=tx&chl=%20%28a%20%2B%20b%29%5E%5Cwedge%20%3D%20a%20%2B%20b%5E%5Cwedge)
(2-2) ![a + 0^\wedge = (a + 0)^\wedge](https://chart.apis.google.com/chart?cht=tx&chl=%20a%20%2B%200%5E%5Cwedge%20%3D%20%28a%20%2B%200%29%5E%5Cwedge)
(2-3) ![a + 0^\wedge = a^\wedge](https://chart.apis.google.com/chart?cht=tx&chl=%20a%20%2B%200%5E%5Cwedge%20%3D%20a%5E%5Cwedge)
(2-4) ![a = 0 + a](https://chart.apis.google.com/chart?cht=tx&chl=%20a%20%3D%200%20%2B%20a)
(2-5) ![(a + 0)' = a + 0'](https://chart.apis.google.com/chart?cht=tx&chl=%20%28a%20%2B%200%29%27%20%3D%20a%20%2B%200%27)
(2-6) ![a + 0' = a'](https://chart.apis.google.com/chart?cht=tx&chl=%20a%20%2B%200%27%20%3D%20a%27)
(2-7) ![a'' = a' + 0'](https://chart.apis.google.com/chart?cht=tx&chl=%20a%27%27%20%3D%20a%27%20%2B%200%27)
(2-8) ![a'' = a' + 1](https://chart.apis.google.com/chart?cht=tx&chl=%20a%27%27%20%3D%20a%27%20%2B%201)
(2-9) ![a' = a + 1](https://chart.apis.google.com/chart?cht=tx&chl=%20a%27%20%3D%20a%20%2B%201)
(2-10) ![a^\wedge + 1 = (a + 1)^\wedge](https://chart.apis.google.com/chart?cht=tx&chl=%20a%5E%5Cwedge%20%2B%201%20%3D%20%28a%20%2B%201%29%5E%5Cwedge)
(2-11) ![(0 + 1)^\wedge = 0^\wedge + 1](https://chart.apis.google.com/chart?cht=tx&chl=%20%280%20%2B%201%29%5E%5Cwedge%20%3D%200%5E%5Cwedge%20%2B%201)
(2-12) ![0^\wedge + 1 = 1^\wedge](https://chart.apis.google.com/chart?cht=tx&chl=%200%5E%5Cwedge%20%2B%201%20%3D%201%5E%5Cwedge)
(2-13) ![1 + a = a + 1](https://chart.apis.google.com/chart?cht=tx&chl=%201%20%2B%20a%20%3D%20a%20%2B%201)
(3-1) ![(a + 1) + b = a + b'](https://chart.apis.google.com/chart?cht=tx&chl=%20%28a%20%2B%201%29%20%2B%20b%20%3D%20a%20%2B%20b%27)
(3-2) ![a + b^\wedge = a^\wedge + b](https://chart.apis.google.com/chart?cht=tx&chl=%20a%20%2B%20b%5E%5Cwedge%20%3D%20a%5E%5Cwedge%20%2B%20b)
(3-3) ![0 + a^\wedge = 0^\wedge + a](https://chart.apis.google.com/chart?cht=tx&chl=%200%20%2B%20a%5E%5Cwedge%20%3D%200%5E%5Cwedge%20%2B%20a)