On 3 Mrz., 22:19, Virgil <vir...@ligriv.com> wrote: > In article > <cc803d21-3112-4a75-b56b-a4c4ad47a...@gp5g2000vbb.googlegroups.com>, > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 3 Mrz., 00:00, Virgil <vir...@ligriv.com> wrote: > > > In article > > > <4e4bb67d-abca-470f-a4b0-f5d1681d9...@u2g2000vbx.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > > On 2 Mrz., 22:55, Virgil <vir...@ligriv.com> wrote: > > > > > In article > > > > > <1f6ffc0a-1cf2-41cf-9548-73ed71cde...@u2g2000vbx.googlegroups.com>, > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > On 1 Mrz., 22:56, Virgil <vir...@ligriv.com> wrote: > > > > > > > In article > > > > > > > <dcc0a841-b24c-4aba-beac-1358c7692...@h11g2000vbf.googlegroups.com>, > > > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > > On 28 Feb., 22:14, Virgil <vir...@ligriv.com> wrote: > > > > > > > > > > WM confuses those names with the things named. > > > > > > > > > No. > > > > > > > > > > One, two three, and so on, are names . > > > > > > > > > > Ein, Zwei, Drei, und so weiter, are different names but name > > > > > > > > > the > > > > > > > > > same > > > > > > > > > things. > > > > > > > > > There are rules according to which different names can be put > > > > > > > > together > > > > > > > > to form sentences. These rules belong to mathematics. > > > > > > > > For the English language such rules belong to the grammar of the > > > > > > > entire > > > > > > > language, not merely to mathematics > > > > > > > The rule that 2 + 2 can be replaced by 4 belongs to the grammer of > > > > > > English language? > > > > > > The rule that 2 + 2 can be replaced by 4, at least in many contexts, is > > > > > certainly compatible with the rules of English grammmar. > > > > > Is it not compatible with German grammar? > > > > > Don't mistake being compatible with being forced. > > > > 2 + 2 is not forced to be equal to 4 in English, because in the field of > > > integers mod 3, only 0, 1 and 2 occur, no 4 occurs, but 2 + 2 still does > > > and results in 1. > > > So your integers form a field? > > The integers 0,1 and 2 can form a field if the arithmetic is that of > integers modulo 3. > > Note that whether a set of objects forms a field or not depends only on > how the relevant operations of addition and multiplication are defined > on the objects of that set, not on what the members of that set are in > other contexts.
And the multiplicative inverse is not required? Ever heard of a ring without rang and rung?
