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Surjectivity reaches every target. An isomorphism also preserves structure and has an inverse.
Three orders may deliver to two trays: order A reaches tray 1, orders B and C reach tray 2. Every tray is reached, so the delivery map is surjective. Different orders may reach the same tray.
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Both trays have an incoming order. A surjection allows different inputs to share an output; it forbids an unreached output.
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Yes; this map is surjective. Both trays have an incoming order. A surjection allows different inputs to share an output; it forbids an unreached output.
Mapping two different order slips to the same tray is compatible with surjectivity, provided every target tray is reached.
Mathlib · db584cd · Defs.lean
def Bijective (f : α → β) :=Injective f ∧ Surjective f
This definition combines Injective and Surjective using ∧. It shows why the second workshop’s surjectivity conclusion is weaker than bijectivity.
Surjectivity and isomorphisms
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Surjectivity reaches every target. An isomorphism also preserves structure and has an inverse.
Earlier ideas are listed under “Start with these ideas” on this page.
Mapping two different order slips to the same tray is compatible with surjectivity, provided every target tray is reached.
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