I have a funny question - can I call one and only element of singleton the largest number? For example: I have a singleton : $\{1\}$. Can I call 1 the largest number?
Here is what I think: largest number $n$ from set $L$ is a number for which is true $n - k$ (also from $L$) not equal $0$. And if we have not number to compare = 1 is not a largest number. Also here is we have things like: 1 can be as largest as lowest number, largest = lowest?
So can I call 1 the largest number? And if I can't - why?
How do you define the largest element of a set $A$ with respect to partial ordering relation $\le$ on it?
The usual definition is: $a\in A$ is the largest element if and only if $(\forall x\in A)x\le a$. This is satisfied for the only element $a$ in a singleton $A=\{a\}$.
What I am guessing is that you are starting with a different definition, e.g. $(\forall x\in A, x\ne a) x\lt a$. ($p\lt q$ means $p\le q$ and $p\ne q$.) In this case, set of those $x$ is empty and you may be confused whether you can claim something is true for all elements of an empty set. Indeed, the very useful convention in math is that you can. This is known as "vacuous truth": something is true "in all cases" because there are no examples where it is false - because there are no examples at all! See: https://en.m.wikipedia.org/wiki/Vacuous_truth .