From cave drawings to navigational charts to GPS, people have created and used maps to help them define, order and navigate their worlds.
Having defined ordered pairs, one can now define ordered triples $(a,b,c)$ as $(a , b,c)$, or in general ordered $n$-tuples $a_11,\ldots,a_n)$ as $a_11, (a_2,\ldots,a_n))$.
Similarly, we can define order versions of other maps discussed in above sections.
For fixedr>0,k∈N∪{0}, define order (r, k) for a quasi-distribution semigroup and define an Fr, kfunctional calculus.
Using our coin example, the actual placement of items is less important than how we define ordered verse disordered.
It is now well established that the sperm changes are progressive and occur in a define order.
As each company and battalion appeared they were pushed forward into the front line, but with no defined orders other than to support the 3rd Brigade.
These defined orders between motifs will help future motif module identification.
The use of purified proteins permits direct interrogation of their functional interaction under controlled conditions across wide concentration ranges using defined orders of addition.
Using the defined order, one can define the majorization [29].
