In the problem we are to show that . Is the ‘2’ here the constant function that sends everything to 2 or what is it? Thanks.

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In the problem we are to show that . Is the ‘2’ here the constant function that sends everything to 2 or what is it? Thanks.

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Yes, in this class, “What is 2?” is a great question.

It is where 2 is the number 2 in the field, and is the multiplicative identity of the incidence algebra, which sends the intervals to 1 and all other intervals to 0.

Silly thought:

Let

and . So isn’t what we are to prove equivalent to

?

I know something is wrong here but What is going wrong? Thanks.

Never mind… that is a very silly mistake I made indeed… -_- (kids,don’t try to do it at home! =D)