# Hasse diagram of a POSET

1. May 5, 2010

### arnold28

Ok I dont understand one thing...We ahd this example in school

We have poset < {1,2,5,7,10,14,35,70}, | >
| meas factor, for example a|b means b=ka, where k=integer

and we got this Hasse diagram

Code (Text):
70
/ | \
10 14 35
| X  X |
2   5  7
\  | /
1
X means crossed lines

But the hasse diagram definition says that we draw a line between element and the element above it if and only if the lower element is the immediate predecessor of the above one. So why is there a line between 1 and 5? Because theres element 2 in between. Same with 1 and 7, 2 and 10, 7 and 35, etc etc same with almost every element. To me they dont seem to be immediate predecessors/successors with each other

I have google some more examples but they all have the same contradiction between definition and example. So what i dont understand here :(

Last edited: May 5, 2010
2. May 5, 2010

### Hurkyl

Staff Emeritus
Really? 1 divides 2 and 2 divides 5?

3. May 5, 2010

### arnold28

i still dont get it :(
for example why is 2 immediate predecessor of 10

Last edited: May 5, 2010
4. May 5, 2010

### Hurkyl

Staff Emeritus
Well, what could come between them? What numbers both divide 10 and are divisible by 2?