Application is not assumed to possess additional properties (such as commutativity), because its intended interpretation is function application. ❋ Bimbó, Katalin (2008)
Now you must give up both commutativity and associativity, but you still have a “division algebra.” ❋ Unknown (2009)
You have to give up commutativity to get the quaternions. ❋ Unknown (2009)
It could well be that there is a way of getting to the quasi-local, infinity-free expansion by solving the spacelike commutativity/anticommutativity requirement directly, but if there is, I have not found it yet. ❋ Sean (2007)
For example the commutativity law x+y = y+x holds for all real values of x and y. ❋ Pratt, Vaughan (2007)
It follows that the non-commutativity of observables imposes limits on the possibilities of joint existence of properties. ❋ Dickson, Michael (2007)
Pruning because of the commutativity of conjunction, we get six combinations: ❋ McNamara, Paul (2006)
For instance, to express the commutativity of addition the user would enter the Lisp expression ❋ Portoraro, Frederic (2005)
A contrary indication is that it is not subject to the rules of change in a legal system -- neither courts nor legislators can repeal or amend the law of commutativity. ❋ Green, Leslie (2003)
The general commander of these regiments gets the informa - ¼ fby commutativity of _g G1 _: G1 _ G2 tion that some soldiers in regiment G3 cannot be ¼ fby definition of complementg G0 _ G2 trusted. ❋ Techdude (2010)
He also proposed a new kind of logic for quantum mechanics that didn't respect commutativity of conjuction and other things. ❋ Unknown (2010)
Mathematics begins with a few basic, autonomous entities (numbers) and a few basic, simple principles (additivity, commutativity, substitutivity), and then allows these to (conceptually) interact. ❋ Unknown (2010)
This statement is absolutely correct … but it is utterly useless to a student who will most certainly not recognize (g 'h g) as a statement about the commutativity of h and g. ❋ Unknown (2009)
One may now recognize that normality really is a weaker analogue of commutativity. ❋ Unknown (2009)
Speaking of defining normal subgroups, it is really inexcusable how many students have never even noticed the close relationship between normal subgroups and commutativity. ❋ Unknown (2009)
We're really talking about commutativity, but of course our ultimate goal is to be able to blur our eyes (or get sleep-deprived, or drunk) such that we can't tell the difference between the members of H. ❋ Unknown (2009)
Use the commutativity of (xD - b) and (xD - a) to find a fundamental set of solutions in the case that a and b are real and distinct. ❋ Unknown (2009)
; Real Function Algebras offers results of independent interest such as: topological conditions for the commutativity of a real or complex Banach algebra; Ransford's short elementary proof of the Bishop-Stone-Weierstrass theorem; the implication of the analyticity or antianalyticity of f from the harmonicity of Re f, Re f (2), Re f (3), and Re f (4); and the positivity of the real part of a linear functional on a subspace of C (X). ❋ Unknown (2009)
