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What do Algebra and Calculus mean?

Where are the numbers? derivatives? integrals? limits? If I understand it correctly, lambda calculus is all about symbols. There are no numbers or operators like addition or multiplications except in a very abstract way like Church encoding and alike. The way I see it, it has nothing to do with what we called calculus in high school or university. Insights?

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marked as duplicate by MJD, Qiaochu Yuan Oct 20 '12 at 19:19

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It's a "calculus" in the sense of a system of manipulations (like "logical calculus"), not a "calculus" in the sense of "differential calculus" that you're thinking of. – Alex Nelson Oct 20 '12 at 18:15
If compact Hausdorff spaces are normal, how come $\beta\mathbb N$ is so crazy? :-) Names are just words. – Asaf Karagila Oct 20 '12 at 19:14

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Calculus is here what would be called Kalkül in German or calcul in French, coming from latin calculus "stone (used for computation)" and denotes a formal system of rules. Thus lambda calculus is not the same as calculus in the sense of differential and integral calculus (which e.g. in German is called Differential- und Integralrechnung, not Differential- und Integralkalkül)

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