What is the point of a less or canceled equal operator?

Question

In my computing science script there is a really weird symbol:

What does this symbol mean? Is it any different from '<'? Is this just to higlight the fact that it is not equal? I'm confused ...

Edit: I should mention that R(N,m_0) is a graph (V,E) and m1,m2 element of V.

Answer 1

In this symbol list, it is called "LESS-THAN AND SINGLE-LINE NOT EQUAL TO", $\lneq$. There is also "GREATER-THAN AND SINGLE-LINE NOT EQUAL TO", $\gneq$. These are apparently variants on $\lneqq$ and $\gneqq$, so your interpretation of smaller than but not equal to is likely correct.

Answer 2

This is usually used in special situations where $<$ does not mean strictly less than. One example I know is in topology, where $\subset$, which in most subjects indicates a proper subset, means simply a subset of, and could be equal. In that case you use $\subsetneq$ in the case where you need to specify that the subset is proper. This is rare in topology, hence the notation.

The author could also be simply emphasizing that it is not equal even though $<$ could mean the same thing.