How can it be true that $5\geq -2$? I know that it is true that $5\geq  -2$, but I really do not understand why. Let me explain how I think. 

$5\geq -2$ means that $5$ is greater than or equal to $-2$. I am perfectly fine with the fact that $5$ is greater than $-2$. I am not so fine with the fact that $5=-2$, as $5\neq -2$. I think that I have misunderstood something in the concept of inequalities. 

With consideration to what I have written in the quote, why is it true that $5\geq -2$? 
 A: "I am from earth, or I am a martian" is a true statement about me, because I am from earth. Once you know that, whatever follows the "or" is irrelevant, because "A or B" means that either A is true, or B is true, or that both are true. (The latter is the rule in mathematics; in common language this last case is sometimes implicitly ruled out.) 
If I had written 
"I am from earth, and I am a martian," it would have been false, for "A and B" requires that both A and B be true, and since I am not a martian, the second condition fails.
With this in mind, consider once again "$5$ is larger than $-2$ or $5$ is equal to $-2$." This statement is true because the first clause is true, regardless of the truth of the second clause. 
In short, it's all about the meaning of the word "or", not about equality and inequality.  
A: The following implication is false:
$$x \leq y \quad \Rightarrow \quad x = y$$
However, the converse is true.
A: The meaning of the symbol "$\ge$" is "greater or equal" that is
$$5\ge -2 \iff 5>-2 \lor 5=-2$$
thus since $5>-2$ is true then $5\ge -2$ is also true.
A: $\geq$ is greater than OR equal to.  If it were greater than AND equal to, you would be right in thinking there were a problem.
