Anyways, despite my laughable amount of knowledge on rings, I managed to reach this conclusion : if we denote " e " as the additive identity of this ring, then x + x = " e " for any arbitrary element x.
22.
I'm kind of suck on a question where I have to prove that a common divisor of the highest degree of two arbitrary elements f ( x ) and g ( x ) in the polynomial ring, lets call it h ( x ).
23.
Therefore, it cannot be that every \ boldsymbol { \ Pi } ^ 0 _ 1 set must be " more definable " than an arbitrary element of a Polish space ( say, an arbitrary real number, or an arbitrary countable sequence of natural numbers ).
24.
In a few species, such as lyrebirds and mockingbirds, songs imbed arbitrary elements learned in the individual's lifetime, a form of mimicry ( though maybe better called " appropriation " [ Ehrlich et al . ], as the bird does not pass for another species ).
25.
In mathematics, in reference to an arbitrary element ( e . g ., a human, an object, a computer ), within a well-defined set ( called the " anonymity set " ), " anonymity " of that element refers to the property of that element of not being identifiable within this set.
26.
Computation proceeds by picking an arbitrary element " x " of the group modulo " N " and computing a large and smooth multiple " Ax " of it; if the order of at least one but not all of the reduced groups is a divisor of A, this yields a factorisation.
27.
A new Asian line-up consisting of Shyaithan, Arbitrary Element's Tremor ( drums ), Dusk's Iron Shaikh ( bass ) and Absence of the Sacred's Mike Priest ( guitars ) was brought together and resulted in the " Tormentors of Tijuana " live album on Japan's cult Heavy Metal Super Star Records ( 2007 ) and the studio effort " Formidonis Nex Cultus ", once again for Agonia.
