- Axioms & Definitions
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- Circularity in mathematics & 'Paradoxes' resolved
- Building blocks & Incompleteness theorems
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Rigour with intuition
- Reals & Real exponentiation & $\cos,\sin$ & $\exp(iπ)+1=0$
- General differentiation & applications
- Matrix multiplication
- For k-times-differentiable functions
- Central difference formulae
- Newton-Raphson with convergence criteria
- Systematic computation of limits
- To prove AM-GM & Jensen's inequality
- Maximum area of polygon given perimeter
- Maximum expression value using brackets
- Multi-dimensional IVT, which proves:
- Poincaré–Miranda theorem
- Ham sandwich theorem [consider all hyperplanes that bisect one piece]
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