 Importantly, due to the logical techniques used in its construction, Robinson’s system behaves exactly like the standard finite real numbers for any sentence expressible within the algebraic language of addition and multiplication. Thus, every number other than 0 has a multiplicative inverse, and if \(x &gt; y\), then \(1/y &gt; 1/x\). In particular, this means that if \(\epsilon\) is a positive infinitesimal number, then \(1/\epsilon\) is an infinitely large number! Unlike Cantorian infinities of counting from section  3.3  these infinitely large numbers are subject to subtraction and division as well as addition and multiplication, and unlike the infinities of the extended real line from section  3.2,  they behave just as nicely as the finite numbers with respect to them. For instance, statements such as these hold of standard real numbers as well as of the new infinitely small and infinitely large numbers: