Unlock the Secrets of Math: 15 Essential Concepts You Need to Know

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p-adic absolute value, 140

p-adic numbers, 137

p-adic ordinal, 139

parallelogram equality, 164

partially ordered set, 19

Picard’s theorem, 183

plane wave function, 237pointwise convergence, 191

polar coordinates, 278

pole of order \(m\), 364

power series, 296

power set, 3

projection, 18

Pythagorean theorem, 151

quotient set, 18

quotient space, 17

radius of convergence, 296

ratio test, 59

real numbers, 29

relation, 15

removable singularity, 364

residue, 366

residue theorem, 368

reverse triangle inequality, 35

Riemann integrable function, 112,

241

Riemann mapping theorem, 319

Riemann sphere, 287

Riemann sum, 111

Riemann surface, 311

Riesz representation theorem, 159

Rolle’s theorem, 102

roots of unity, 285

root test, 60

Russell’s paradox, 2

Schroder-Bernstein theorem, 11

Schwarz’ Lemma, 357

second category, 147

sector, 281

separable, 203

sequence space, 164

sequentially compact, 143

set

closed, 65, 131

dense, 146

diameter, 173

empty, 21

nowhere dense, 146

open, 63, 131

simple function, 250

simply connected, 319