Content deleted Content added
→Unclear statement: new section |
|||
Line 25:
"''Note that because of the second condition, power series are used here only to allow infinitely many terms of a fixed degree, rather than to sum terms of all possible degrees. Allowing this is necessary because an element that contains for instance a term X<sub>1</sub> should also contain a term X<sub>i</sub> for every i > 1 in order to be symmetric.''"
I do not understand why Condition 2. is "necessary", as the second sentence claims. Yes, it is clear that "''an element that contains for instance a term X<sub>1</sub> should also contain a term X<sub>i</sub> for every i > 1 in order to be symmetric''" — but what does this have to do with Condition 2. ???
Obviously, the subring of formal power series in infinitely many indeterminates X<sub>i</sub> defined solely by Condition 1. — which requires that they are unchanged by the action of the permutation group S('''ℕ'''<sub>0</sub>) of the nonnegative integers '''ℕ'''<sub>0</sub> on the indices — makes perfect sense. So this defines a subring that does not require Condition 2.
| |||