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Definition df-aa 20224
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 20223 . 2  class  AA
2 vf . . 3  set  f
3 cz 10274 . . . . 5  class  ZZ
4 cply 20095 . . . . 5  class Poly
53, 4cfv 5446 . . . 4  class  (Poly `  ZZ )
6 c0p 19553 . . . . 5  class  0 p
76csn 3806 . . . 4  class  { 0 p }
85, 7cdif 3309 . . 3  class  ( (Poly `  ZZ )  \  {
0 p } )
92cv 1651 . . . . 5  class  f
109ccnv 4869 . . . 4  class  `' f
11 cc0 8982 . . . . 5  class  0
1211csn 3806 . . . 4  class  { 0 }
1310, 12cima 4873 . . 3  class  ( `' f " { 0 } )
142, 8, 13ciun 4085 . 2  class  U_ f  e.  ( (Poly `  ZZ )  \  { 0 p } ) ( `' f " { 0 } )
151, 14wceq 1652 1  wff  AA  =  U_ f  e.  ( (Poly `  ZZ )  \  {
0 p } ) ( `' f " { 0 } )
Colors of variables: wff set class
This definition is referenced by:  elaa  20225
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