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/sci/ - Science & Math

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>> No.11430871 [View]
File: 149 KB, 462x484, __fujiwara_no_mokou_touhou_drawn_by_shangguan_feiying__22aed64f9c510097f66bbb4c637be7e4.jpg [View same] [iqdb] [saucenao] [google]
11430871

>>11430855
Jesus fucking Christ.
We have that [math]inf ~ U(f, P) - sup ~ L(f, P) \leq U(f, P) - L(f, P) < \epsilon[/math], by the literal definition of infima and suprema, and since it's for all [math]\epsilon[/math], we have [math]inf ~ U(f, P) - sup ~ L(f, P) = 0[/math].

>> No.11383567 [View]
File: 149 KB, 462x484, __fujiwara_no_mokou_touhou_drawn_by_shangguan_feiying__22aed64f9c510097f66bbb4c637be7e4.jpg [View same] [iqdb] [saucenao] [google]
11383567

>>11382913
Did you try telling them that the point of the axiom of induction isn't to make proofs by induction possible, but to ensure the naturals are "small", which coincidentally allows for induction?

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