Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with alternative-proof
Search options not deleted
user 75215
Looking for a proof different from the standard proof(s) of a result
6
votes
Slick proof?: A vector space has the same dimension as its dual if and only if it is finite ...
Here is a proof for $\dim(V^*)>\dim(V)$ for every infinite dimensional vector space $V$ over a field $k$. More precisely, we prove that
$$\mathrm{dim}(V^*)=|V^*|=|k|^{\dim(V)}\geq 2^{\dim(V)}>\dim(V). …