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Clash Royale CLAN TAG #URR8PPP up vote 0 down vote favorite ∃y ∈ Z such that ∀x ∈ Z, R(x + y) ∀x ∈ Z, ∃y ∈ Z such that R(x + y) Base on this two rule "For all x, A(x)" negation:"There exist x such that not A(x)" "There exists x such that A(x)" negation:"For every x, not A(x)" what I did is "∀y ∈ Z, not ∀x ∈ Z, R(x + y)" "∃x ∈ Z, ∀y ∈ Z such that R(x + y) " I wish anyone could help me to check whether this is right or not. Th...

Clash Royale CLAN TAG #URR8PPP up vote 8 down vote favorite 2 It appears to be a standard fact in topology that $mathbbCmathbbP^2#-mathbbCmathbbP^2$ has a structure of a $mathbbS^2$ bundle over $mathbbS^2$. Is there a nice geometric description of the projection to the sphere? This manifold is actually a complex algebraic variety (namely a plane with one point blown up), so the question should make some sense. The best answer would probably be a meromorphic function, but I could not find one. reference-request dg.differential-geometry share | cite | improve this question asked Aug 19 at 9:58 Alex Gavrilov 3,116 11 36 add a comment  |  up vote 8 down vote favorite 2 It appears to be a standard fact in topology that $mathbbCmathbbP^2#-mathbbCmathbbP^2$ has a structure of a $mathbbS^2$ bundle over $mathbbS^2$. Is there a nice geometric description of the projection to the sphere? This manifold is actually a co...