執二攤~之~Fixed Point Theorem?


細佬的三歲童裝褲又開始緊。

「家姐妳來試試……喜歡這條褲嗎?……緊嗎?」

「少少。」

「哎唷,爹爹你看,家姐如此愛抱細佬,慘啦,我懷疑有一天細佬終會比家姐重!?」

「何需懷疑,肯定發生啦,那是Fixed Point Theorem。」

IMG_9108 IMG_9117 IMG_9124

好了,嚴格來說我認為那不是Fixed Point Theorem。要用Fixed Point Theorem,就得首先假設細佬一定最終會長得比家姐重,然後告訴媽媽,總有一天,兩隻生番能穿上同一條(fixed point)褲。

weights

(Miss Chan Chan,妳在哪裡?)

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10 responses to “執二攤~之~Fixed Point Theorem?

  1. mokmok

    “就得首先假設細佬一定最終會長得比家姐重"
    嗯…阿四出了一題命題考讀者
    不才認為人的體重係漸近一個體重,取決於Y-intercept,如果假設同時期體重的slope係一樣(環境不變吧!),咁應該會證得命題.

  2. Miss Chan Chan

    Not sure if economist, engineer or mother group have another fixed point theorem??
    If my interpretation is correct, the key relationship in fixed point theorem is:
    there exists a x such that f(x) = x .
    Graphically, y = f(x) and y = x will intersect.
    So,.. your graph or title might be misleading if there is no other fixed point theorem.

    • sorry i was indeed misleading- my graph was just a plot of the reality. wasn’t trying to prove a theorem 🙂
      in fact i have還番晒Dtheorems俾你already 😉

      • Simon Ching

        The function in question, h, is f – g where f and g are masses of 小C’s and 細佬 respectively; and the domain of h we are concerned is [a, b] where a = epoch – delta and b = epoch + \tilde{delta}] where delta, \tilda{delta} > 0. And epoch is, of course, the time when 細佬 has the same mass as 小C. Btw, you might want to put a cap on b, say, 5 years from now, for the discussion to be meaningful: cause you don’t expect the siblings to exchange clothes when they are, say, in their twenties? (And even if they do, it’s not of your real concern when you won’t be saving money, which I assume is your real point of discussion)

        You are right, Mama4, for Fixed Point Theorem to be applicable you have to have h(a) * h(b) < 0, which is not guaranteed.

        Btw, we didn't cover Fixed Point Theorem back in secondary school did we?

  3. 唔,睇怕有一天阿包都會跟我穿同一條尺寸的褲。

  4. Simon Ching

    Oops, the function of concern should be h – g + epoch instead.🙂

    • Simon Ching

      囧, error again. f – g + epoch, not h – g + epoch…
      And the condition for applicability of the theorem should be h(a) * h(b) – epoch (h(a) – h(b)) + epoch^2 < 0

  5. Miss Chan Chan

    Their growth curves (in terms of mass or height) of your two lovely kids will probably intersect a few times before they become adults.
    BTW, you probably encounter the idea of fixed point theorem when you studied Pure Math. Fortunately, I was not your P.M. teacher, so you didn’t return it to me.

  6. 野蠻九龍女

    阿四你好. 我個女出左世啦. 同你一樣, 阿女係細碼; 阿仔超大碼……

    阿仔爸爸依家成日講, 真好彩, 一個唔覺意調轉左, 阿女係大碼; 阿仔係細碼…….. 就陰公羅…..

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