# How does Perfect Elasticity imply infinite quantity for any higher price?

I reference Principles of Microeconomics, 7 Ed, 2014, by NG Mankiw. The graph above is from p 100.

[p 99:] ...supply is perfectly elastic. This occurs as the price elasticity of supply approaches infinity and the supply curve becomes horizontal, meaning that very small changes in the price lead to very large changes in the quantity supplied.

Please explain the red box? How's it true? The graph itself shows that at \$4 exclusively, all quantities$\ge 0$are supplied. The graph depicts nothing for prices above \$4? (Footnote: I tried this)

More formally, "any quantity" does not mean "infinite quantity" because "infinity" is not a number, so it cannot represent a quantity (and let's not confuse quantity with the concept of cardinality used in set theory). The expression $x\geq 0$ does not include "$\infty$". $x$ belongs to the real numbers, and $\infty$ is added to the real numbers to create the "extended real numbers" - it is not a real number itself.
Perhaps by "logical extension", if all non-zero real quantities are supplied at USD $4$, then what is left for higher prices is only "infinity". But this has no economic meaning -apart from the approximate one already mentioned in the passage quoted.