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Definition df-aa 19695
Description: Define the set of algebraic numbers. An algebraic number is a root of a nonzero polynomial over the integers. Here we construct it as the union of all kernels (preimages of 
{ 0 }) of all polynomials in  (Poly `  ZZ ), except the zero polynomial  0 p. (Contributed by Mario Carneiro, 22-Jul-2014.)
Assertion
Ref Expression
df-aa  |-  AA  =  U_ f  e.  ( (Poly `  ZZ )  \  {
0 p } ) ( `' f " { 0 } )

Detailed syntax breakdown of Definition df-aa
StepHypRef Expression
1 caa 19694 . 2  class  AA
2 vf . . 3  set  f
3 cz 10024 . . . . 5  class  ZZ
4 cply 19566 . . . . 5  class Poly
53, 4cfv 5255 . . . 4  class  (Poly `  ZZ )
6 c0p 19024 . . . . 5  class  0 p
76csn 3640 . . . 4  class  { 0 p }
85, 7cdif 3149 . . 3  class  ( (Poly `  ZZ )  \  {
0 p } )
92cv 1622 . . . . 5  class  f
109ccnv 4688 . . . 4  class  `' f
11 cc0 8737 . . . . 5  class  0
1211csn 3640 . . . 4  class  { 0 }
1310, 12cima 4692 . . 3  class  ( `' f " { 0 } )
142, 8, 13ciun 3905 . 2  class  U_ f  e.  ( (Poly `  ZZ )  \  { 0 p } ) ( `' f " { 0 } )
151, 14wceq 1623 1  wff  AA  =  U_ f  e.  ( (Poly `  ZZ )  \  {
0 p } ) ( `' f " { 0 } )
Colors of variables: wff set class
This definition is referenced by:  elaa  19696
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