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The two following symbols are called quantifyers:
If is some specific property, the sentence
means that ``for every , the property holds.
If is a property for pairs of objects, the sentence
means that for every , there exists at least one such that holds for and .
- The universal quantifyer: means ``for all'', ``for every'', ... .
- The existence quantifyer: means ``there exists at least one ...''.
The existence quantifyer has an extension, namely , whose meaning is ``there exists exactly one ...''.
The reader understood alreday that the vertical bar
means ``such that''. Sometimes we use a semicolon ``;'' instead of