Let $n\in\mathbb{N}$,
can anyone explain me why:
$n+\omega=\omega$ and $n+\omega=\omega$. It makes me crazy. can you explain it me ? For me, it should be $n+\omega = \omega+n$.
Asked
Active
Viewed 68 times
0
Andrés E. Caicedo
- 79,201
Happy man
- 395
-
Check out this post http://math.stackexchange.com/questions/49034/is-infinity-an-odd-or-even-number/49046#49046 – aduh Sep 12 '16 at 15:22
-
You wrote "$n+\omega=\omega$ and $n+\omega=\omega$". Presumably you meant to write something else. – Andrés E. Caicedo Sep 12 '16 at 18:30
-
Why should ordinal addition be commutative necessarily? – Ian Sep 12 '16 at 18:33
-
This youtube video from vsauce explains it intuitively: https://youtu.be/SrU9YDoXE88?t=1386 – Alberto Takase Sep 13 '16 at 00:17
1 Answers
6
$\omega +3$ looks like $$******\cdots **\,*$$ And $3+\omega $ looks like $$*** \ \ ******\cdots$$ where the space is just for emphasis.
So look at the three things:
$$\begin{align*} \omega: &******\cdots\\ 3+\omega: &******\cdots\\ \omega+3: &******\cdots**\,* \end{align*}$$
The first two pictures are the same the third is different.
And anyway what are oodinals ? Is it some kind of noodle ?
Brian M. Scott
- 616,228
Rene Schipperus
- 39,526
-
-
Can you explain me what is ordinal number of $\left{1-\frac{1}{n}:n\in\mathbb{N}\right}\cup \left{2\right}$ ? – Happy man Sep 13 '16 at 08:47
-