A deeper understanding develops when a pattern is generalized algebraically. While applying rules and formulas may be useful, you attain a much deeper level of conceptual understanding when developing rules and formulas. After the rule is developed, then a functions (f(X)) is developed and from there a line with a continuous set of points.
When you generalise algebraically, you are essentially classifying and defining the relationship between each number/set in the pattern or even determining if there is a relationship to begin with.
The verb for generalisation is generalise. As in "to generalise something".
Because they allow you to generalise results. Then, for specific value of the variables you get specific answers.
To generalise
ALGEBRAICALLY : by means of ALGEBRA
Algebraically zero
Difficult to generalise, but they're definitely rich...:)
Hitler's health deteriorated, his people were obedient (to generalise).
It is a generalization to say that tall people can play basketball well when, in fact, you need to be able to play well and if you're tall it is an advantage.
Algebraically, a times 2 is 2a.
Each case is inndividual, you can't generalise.
Some do, some don't. It is wrong to generalise.
You get the exact solution.