ChatGPT免費版，還是有簡單的邏輯錯誤

 ChatGPT在經典的問題會答對，
如果三包糖果都裝錯的問題：

如果有三包糖果，一包牛奶口味，一包草莓口妹，一包牛奶和草莓口味都有，三包都裝錯，那最少要嘗試幾顆糖果，才知道這三包糖果各是啥麼口味？

這是經典問題，只需嘗一顆糖果，ChatGPT會答對。

但是只有答案對，一開始論述是錯的。

不過問題改成：

有三包糖果，一包牛奶口味，一包草莓口妹，一包牛奶和草莓口味都有，但是三包都沒有貼標籤，那最少要嘗試幾顆糖果，才知道這三包糖果各是啥麼口味？

ChatGPT就會亂答一通，顯然沒有邏輯。

要回答這題，個人認為題目要給你，一包總共有幾顆？

(但是我問的時候沒給，要ChatGPT自由發揮…)

詳參：

https://chatgpt.com/share/690a9f75-5170-8000-aa26-6c50c615f534

2025/11/24後記，ChatGPT已修正：
https://reurl.cc/NNqRK5

0/0未定義的原因 (小學數學)

0/0是未定義，那為何0/0不是1呢？是否有反例？
我想到的反例如下：(這是我自己想的，如有錯誤，還請指正)
Assume 0/0 = 1,
if 2x = 3x
=> x = 1.5x, so x = 0
=> 0 = 1.5 * 0
兩邊同除0
=> 0/0 =1.5 * 0/0
=> (0/0) = 1.5 * (0/0)
We assume 0/0 = 1
=> 1 = 1.5 * 1
=> 1 = 1.5, 所以這是0/0 = 1的反例

那麼0/0是否等於0呢？
這個我不知道真正的反例，
但是這樣0/0就不能上下消去得到1了。
至於0/0等於其它數值，可以簡單得到反例，
這就不提了。

Differential and Partial differential

Differential of a function

where ${\displaystyle f'(x)}$ is the derivative of f with respect to x, and dx is an additional real variable (so that dy is a function of x and dx). The notation is such that the equation

${\displaystyle dy={\frac {dy}{dx}}\,dx}$

holds, where the derivative is represented in the Leibniz notation dy/dx, and this is consistent with regarding the derivative as the quotient of the differentials. One also writes

${\displaystyle df(x)=f'(x)\,dx.}$

satisfies

${\displaystyle \Delta y=f'(x)\,\Delta x+\varepsilon =df(x)+\varepsilon \,}$

where the error ε in the approximation satisfies ε/Δx → 0 as Δx → 0. In other words, one has the approximate identity

${\displaystyle \Delta y\approx dy}$

in which the error can be made as small as desired relative to Δx by constraining Δx to be sufficiently small; that is to say,

${\displaystyle {\frac {\Delta y-dy}{\Delta x}}\to 0}$

as Δx → 0. For this reason, the differential of a function is known as the principal (linear) part in the increment of a function: the differential is a linear function of the increment Δx, and although the error ε may be nonlinear, it tends to zero rapidly as Δx tends to zero.

the partial differential of y with respect to any one of the variables x₁ is the principal part of the change in y resulting from a change dx₁ in that one variable. The partial differential is therefore

${\displaystyle {\frac {\partial y}{\partial x_{1}}}dx_{1}}$

參：

https://en.wikipedia.org/wiki/Differential_of_a_function

全微分和偏微分有什麼不同

假設 z = x^7 + y^3 + 3(x^2)*(y^4) + 4xy + 98 
z為應變數 , x y為自變數 

全微分 : 
就是所有變數通通都要微分 
dz = 7x^6dx + 3y^2dy + 6x(y^4)dx + 12(x^2)*(y^3)dy + 4ydx + 4xdy + 0 
ps. 兩變數相乘的 , 如同一般乘法的微分 , 前微後不微+前不微後微 

偏微分 : 
只對要微的自變數微分 , 其他的都當作常數 
1.對 x 偏微 
∂z/∂x = 7x^6 + 0 + 6x(y^4) + 4y + 0 

2. 對 y 偏微 
∂z/∂y = 0 + 3y^2 + 12(x^2)*(y^3) + 4x + 0

參：

https://tw.answers.yahoo.com/question/index?qid=20050930000013KK04937