The actual infinite arises in ...

The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type.
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 Georg Cantor

Quotes from the same author

A false conclusion once arrived at and widely accepted is not easily dislodged and the less it is understood the more tenaciously it is held.
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 Georg Cantor
Mathematics, in the development of its ideas, has only to take account of the immanent reality of its concepts and has absolutely no obligation to examine their transient reality.
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 Georg Cantor
Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.
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 Georg Cantor