I think maybe you're confusing a specialist mage with a sorcerer.
A specialist mage (Diviner, Illusionist, Necromancer etc) is allowed one extra spell per level but can't learn spells from its school of opposition.
A sorcerer has the innate ability to cast spells, they dont need to select and prepare them. They know fewer spells and acquire them more slowly but can cast them more often. Sorcerers dont need to memorize spells.
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It's bleedin dark down here, slippery too.

Man, that's a pisser.