# Thread: n+w is w, bt w+n is not w. Why?

1. ## n+w is w, bt w+n is not w. Why?

cannot comprehend this from my text book. How to understand this?

Consider the order types w and n. It is easy to see that n+w=w. In fact, if finitely many terms are written to the left of the sequence 1,2,...,k,..., we again get a set of the same type(why?). On the other hand, the order type w + n, i.e., the order type of the set {1,2,...,k,...,a1,a2,...,an} is obviously(?) not equal to w.

2. Why: Because the textbooks can be wrong.

If
n+w = w
Then it is a MUST that
w+n =w

Why: Because the textbooks can be wrong.
If n+w = w Then it must be true that w+n =w
What if this is a noncommutative operation symbolized by ‘+’?

4. Originally Posted by Plato
What if this is a noncommutative operation symbolized by ‘+’?
I accept it
EDIT: What Plato says is correct, it could be any other non-commutative function or rather it should be

non-commutative operation
The result of operation depends on the order
eg; Substraction

$\displaystyle a-b \ne b-a$

untill $\displaystyle a = b$

5. Originally Posted by ninano1205
cannot comprehend this from my text book. How to understand this?
We need more information. What are n and m? Are they numbers? Is "+" the usual addition of numbers or is it defined differently?

6. Originally Posted by Plato