Content deleted Content added
Line 55:
for each ''n'' = 1, 2, ... Complete this sequence of linearly independent vectors to a [[basis (vector space)|vector space basis]] of ''X'', and define ''T'' at the other vectors in the basis to be zero. ''T'' so defined will extend uniquely to a linear map on ''X'', and since it is clearly not bounded, it is not continuous.
Notice that by using the fact that any set of linearly independent vectors can be completed to a basis, we implicitly used the axiom of choice, which was not needed for the concrete example in the previous section but one.
== Axiom of choice ==
| |||