有向數及數線 | Directed Numbers and Number Line

影片內容:

00:05 – 負數 | negative numbers
01:35 – 有向數 | directed numbers
02:54 – 數線 | number line

19 Comments
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Excuse me, may I ask why 0!=1? Thank you.

Excuse me, may I ask why 0!=1?

If there is a tank of length, width, height of 40x10x30 respectively, and there are 8L of water in the tank. Then put a prism of base area 80cm square, height 60cm.The base of the prism touch the bottom of the tank.
Will the water overflowing???

the capacity of the tank: 40x10x30=12000ml=12L,
the volume of prism: 80x60x1/3=1600ml=1.6L
the capacity of the tank > the volume of prism+8L
the water won’t overflowing

Why (-2)^0.1 =1.01931714 + 0.331196214 i ?

Is π digits random? (which means each digit appears very close to 10% of the time or not)

IDENTITY (Administrator) 13/06/2021 at 14:18

好有趣嘅問題,之前都冇諗過。上網見到呢篇 blog 寫得唔錯,結論係:未有 mathematical proof 證明到係 uniformly distributed (i.e. 10% chance of appearance),但 empirical evidence 似乎話畀我哋知真係 10% chance。

https://blogs.sas.com/content/iml/2015/03/12/digits-of-pi.html

how do i rationalise the denominator \frac{1}{\sqrt{12}}

IDENTITY (Administrator) 24/01/2021 at 01:01

Haha 你竟然知道呢度可以用 LaTeX。返返你嘅問題:

     \begin{align*} \frac{1}{\sqrt{12}}&=\frac{1}{\sqrt{12}}\times\frac{\sqrt{12}}{\sqrt{12}}\\ &=\frac{\sqrt{12}}{12}\\ &=\frac{\sqrt{3\times4}}{12}\\ &=\frac{\sqrt{3}\times\sqrt{4}}{12}\\ &=\frac{\sqrt{3}\times2}{12}\\ &=\frac{\sqrt{3}}{6} \end{align*}

IDENTITY (Administrator) 11/10/2020 at 14:26

Haha a little surprise to the old IDENTITY users. Which one do you like better 🙂 ?

The new one of course!

Is 0 a directed number?

IDENTITY (Administrator) 11/10/2020 at 14:20

Short answer: I don’t think there’s a clear definition on that.

In fact, directed number is not a very rigorous mathematical definition. It’s just a fancy term to emphasize a number can be positive or negative. In that sense, arguing whether 0 is a directed number may not be very meaningful. After all, +0 = -0 = 0.

x(x-2)+A(x-1)≡x^2+B find the value of A and B

I don’t know how to do this question

IDENTITY (Administrator) 11/10/2020 at 14:23

Sorry for the late reply.
You’re right. A = 2 and B = -2. Well done!

Anyone could explain the Mandelbrot Set?

IDENTITY (Administrator) 11/10/2020 at 14:28

That’s beyond our knowledge. Hopefully some mathematicians will pass by and explain a bit~

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