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**MathCrusader** How would one, as intuitively as possible, explain *why* the following implication is false

$\displaystyle x \geq 4 \ \Rightarrow \ x > 4 \, .$

I understand that for $\displaystyle x \geq 4$ either the statement $\displaystyle x = 4$ or $\displaystyle x > 4$ must be true. Suppose the statement $\displaystyle x = 4$ is true; the falsity of the implication is quite apparent then. If the statement $\displaystyle x > 4$ is true then the veracity is apparent. Thus the implication is only true for one statement of the two within $\displaystyle x \geq 4$.

However, the following implication is surprisingly true:

$\displaystyle x > 4 \ \Rightarrow \ x \geq 4 \, .$

How come? Suppose $\displaystyle x = 4$ on the right-hand side of the implication is true; that implication is false! The implication is only true if $\displaystyle x > 4$ on the right-hand side. Once again, the implication is only true for *one* statement of the two within $\displaystyle x \geq 4$. In spite of this, we still claim that the implication as a whole is true whereas the first one is not.