Alba 🌸 :v_pat: on Nostr: 0xa1baa1baa1baa1ba it depends heavily on context, but "number system" usually means ...
0xa1baa1baa1baa1ba (npub19zq…u4m5) it depends heavily on context, but "number system" usually means "field".
you start by finding a pair of binary operations over a common set. they must "behave well" (be associative) and the 2nd needs to distribute over the 1st.
the 2 operations are usually called "addition" (denoted +) and "multiplication" (denoted ×) respectively.
if this is the case, then the identity element of addition (usually denoted "0") is an *absorbing element* of multiplication. that is, any value applied to this element returns it (a × 0 = 0 × a = 0).
absorbing elements can't be inverted (by definition, because they "swallow" all information).
but in order to call it a "number system", precisely everything else MUST be invertible (this is why we don't call matrices "numbers", because some can't be inverted)
you start by finding a pair of binary operations over a common set. they must "behave well" (be associative) and the 2nd needs to distribute over the 1st.
the 2 operations are usually called "addition" (denoted +) and "multiplication" (denoted ×) respectively.
if this is the case, then the identity element of addition (usually denoted "0") is an *absorbing element* of multiplication. that is, any value applied to this element returns it (a × 0 = 0 × a = 0).
absorbing elements can't be inverted (by definition, because they "swallow" all information).
but in order to call it a "number system", precisely everything else MUST be invertible (this is why we don't call matrices "numbers", because some can't be inverted)