So: what does "<>" mean?
Oh, my...what does "><" mean?
Different disciplines have different conventions.
I work in quantum optics, and we use that notation [itex]\langle x \rangle[/itex] to denote the expectation value (or mean) of the thing [itex]x[/itex] inside the brackets.
Can you show an example of how these are used?
The following quotations are taken from the bottom of the page entitled "Continuity and Limits" From Wyzant <https://www.wyzant.com/resources/lessons/math/calculus/limits/continuity>...
"Intermediate Value Theorem
The Intermediate value theorem states that if we have a continuous function f(x) on the interval [a,b] with M being any number between f(a) and f(b), there exists a number c such that:
1) a < c=""><>
2) f(c) = M...
The Intermediate Value Theorem is a geometrical application illustrating that continuous functions will take on all values between f(a) and f(b). We can see if we draw a horizontal line from M, it will hit the graph at least once. If the function is not continuous on the interval, this theorem would not hold.
It is important to note that this theorem does not tell us the value of M, but only that it exists. For example, we can use this theorem to see if a function will have any x intercepts.
(1) Use the Intermediate Value theorem to determine if f(x) = 2x3 - 5x<> - 10x + 5 has a root somewhere in the interval [-1,2].
In other words, we are asking if f(x) = 0 in the interval [-1,2]. Using the theorem, we can say that we want to show that there is a number c where -1 < c="">< 2="" such="" that="" m="0" in="" between="" f(-1)="" and="">
We see that p(-1) = 8 and p(2) = -19. Therefore, 8 > 0 > -19, and at least one root exists for f(x)."
Note: I didn't bother with the grammatical tedium of putting the above quotations into proper nested quotes. But you can see the various "<>" and "><" quoted. What do these mean?
Looks like (typesetting?) errors on that webpage.
For example, this one:
was meant to be 1) ##a<c<b##
As far as I can tell, and looking at the web page you cited, it's meaningless. Most likely some weirdness in the web page. Same with the other ones you cited.
My guess is the editor used to create the page had an auto completion feature meaning when you type < then it adds > immediately similarly for quotes and other special paired characters.
As an aside, In Basic and some other programming languages <> can mean "not equal to".
I'm inclined to agree with Samy_A that the page in question has some typos. This inequality, 1) a < c=""><>, is just gibberish. And the same for the other stuff cited.
Some code-tagging systems use the two characters to surround a tag, like <s>something expressed</s> will put a "strike through" dash through the tagged expression; that is left arrow, s, right arrow, something expressed, left arrow, forwardslash, right arrow.
Also, as jedishru said, "unequal" between two number or string expressions or variables, for some computer programming languages like BASIC.
Separate names with a comma.