from Wiktionary, Creative Commons Attribution/Share-Alike License
- adv. Using algebra.
from the GNU version of the Collaborative International Dictionary of English
- adv. By algebraic process.
from The Century Dictionary and Cyclopedia
- By means of algebra, or of algebraic processes; in an algebraic manner; as regards algebra.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
- adv. in an algebraic manner
And even those foreign correspondents who are tragically wounded or killed most years are an algebraically smaller number than the local journalists murdered for doing their jobs.
The omission of "degree" indicates that it is not relative to an arbitrary reference point like the Celsius and Fahrenheit scales, but rather an absolute unit of measure which can be manipulated algebraically.
Leaving aside the question of how many bikes is appropriate (an easy question to answer algebraically, by the way: when x is the appropriate number and b is the number of bikes you have now, then x = b+1), the question of how many are actually on site here on North Upper is addressed in passing in a front page article in today's Lexington Herald-Leader.
The omission of "degree" indicates that it is not relative to an arbitrary reference point like the Celsius and Fahrenheit scales — both of which should have the adjective prefix "degrees" — but rather an absolute unit of measure which can be manipulated algebraically; e.g., multiplied by two to indicate twice the amount of "mean energy" available among elementary degrees of freedom of the system.
For at least four reasons, which I will name algebraically.
In this way one can characterize the operations of infinitesimal analysis algebraically but without any of the naÃ¯vetÃ© which had characterized the previous algebraic approaches.
Around 1950 Abraham Robinson was impressed that maps between algebraic structures in general seem hardly ever to be elementary, whereas some important maps (such as embeddings between two algebraically closed fields, or between two real-closed fields) turn out to be elementary.
He was also surprised to find that this fact about algebraically closed fields is another way of stating a celebrated theorem called the Hilbert Nullstellensatz.
Given this, our only real option is to fall back on some form of axiomatized set theory, and the only respectable way to understand our axioms is algebraically (since understanding them intuitively would amount to falling back into our previously discredited naivetÃ©).
Such a mixture could be described algebraically as a violation of the Completeness Principle, or semantically as a violation of the Axiom of Restricted Comprehension.