field
is the set of all tuples of length 
of elements of 
:
for 
and 
, we say that 
is the kth coordinate of 
.[cite:;taken from @algebra_axler_2024 chapter 1 vector spaces; definition 1.11]
addition in 
is defined by adding corresponding coordinates:
[cite:;taken from @algebra_axler_2024 chapter 1 vector spaces; definition 1.13]
is defined by adding corresponding coordinates:[cite:;taken from @algebra_axler_2024 chapter 1 vector spaces; definition 1.13][cite:;refer to @analysis_cummings_2019 chapter 1 the reals; definition 1.5]