Changes

*the '''hyperreals''': denoted ^*<math>\mathbb{R}</math>, these extend the real numbers with both infinite and infinitesimal quantities. They are used in non-standard analysis. Other extensions of the real numbers with infinite and infinitesimal quantities include the '''surreal numbers''', the '''superreal numbers''', and the '''Levi-Civita field'''.

*the '''hyperreals''': denoted ^*<math>\mathbb{R}</math>, these extend the real numbers with both infinite and infinitesimal quantities. They are used in non-standard analysis. Other extensions of the real numbers with infinite and infinitesimal quantities include the '''surreal numbers''', the '''superreal numbers''', and the '''Levi-Civita field'''.

The conclusion to be drawn from all of this, is that although in popular usage we speak about ''infinity'' as if it were a single thing, there are actually numerous diferent infinities, all belonging to different systems. If we want to talk about ''infinity'', we ought to be careful to specify which infinity we mean. In this light, claims such as ''God is infinite'' are particularly incomprehnsible, because those who propose them never define which infinity they are using to describe God, or in what way that infinity describes him.

The conclusion to be drawn from all of this, is that although in popular usage we speak about ''infinity'' as if it were a single thing, there are actually numerous diferent infinities, all belonging to different systems. If we want to talk about ''infinity'', we ought to be careful to specify which infinity we mean.

==Archimedean property==

==Archimedean property==