Lîm Tsú-thuàn :unverified: on Nostr: 令 ε ≠ 0, ε^2 = 0 f(x) = x^2 + 2x + 3 f(x + ε) = (x + ε)^ 2 + 2x + 2ε + 3 = ...

令 ε ≠ 0, ε^2 = 0

f(x) = x^2 + 2x + 3
f(x + ε)
= (x + ε)^ 2 + 2x + 2ε + 3
= x^2 + ε^2 + 2εx + 2x + 2ε + 3
= x^2 + 2x + 3 + 2εx + 2ε
= (x^2 + 2x + 3) + ε(2x + 2)

熟悉微分的人應該已經看出這裡發生了什麼

這也可以視為一維度的格拉斯曼代數
https://en.wikipedia.org/wiki/Dual_number