Mathematic Glossary - I to Q

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I To Q

164

image

165

image of compact set under continuous function

166

image of connected set under continuous function

167

increasing function

168

induction principle

169

induction, axiom

170

induction, proof by

171

infimum

172

infimum of sequence

173

infinite series

174

injection

175

integers

176

integral evaluation shortcut

177

integral test for series

178

integrating power series

179

integration and uniform convergence

180

integration by parts

181

integration by parts and limits

182

interior and boundary

183

interior points

184

intermediate value theorem

185

intersection

186

intersection of closed sets

187

intersection of open sets

188

inverse image

189

inverse image of closed set under continuous function

190

inverse image of open set under continuous function

191

isolated points

192

isolated points and accumulation points

193

jump discontinuity

194

l'Hospital's rule

195

Lagrange remainder

196

Leaning Tower of Lire

197

least upper bound

198

least upper bound property

199

Lebesgue integrable versus Riemann integrable

200

Lebesgue integral, bounded functions

201

lebesgue Integral, general

202

Lebesgue integral, non-negative Ffunctions

203

Lebesgue integral, properties

204

Lebesgue integral, simple function

205

Lebesgue measure

206

Lebesgue measure, non-measurable set

207

Lebesgue measure, properties

208

Lebesgue's Bounded Convergence theorem

209

left-hand limit

210

lim inf

211

lim inf and limit

212

lim inf, existence

213

lim inf, properties

214

lim sup

215

lim sup and limit

216

lim sup, existence

217

lim sup, properties

218

limit comparison test for series

219

limit from the left

220

limit from the right

221

limit inferior

222

limit of function (epsilon-delta)

223

limit of function (sequences)

224

limit of sequence

225

limit superior

226

limit, one-sided

227

limits and continuity

228

limits and lim sup, lim inf

229

limits and one-sided limits

230

limits, sequences, and epsilon-delta

231

Lipschitz functions

232

Lire, Leaning Tower of

233

local extrema, derivatives, and monotonicity

234

local extremum

235

local maximum

236

local minimum

237

lower bound

238

lower sum

239

lower sum as increasing operator

240

MacLaurin series

241

maximum theorem for continuos functions

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maximum, local

243

mean value theorem

244

mean value theorem for integration

245

measurable function

246

measurable functions, almost continuous

247

measurable sets

248

measurable sets, monotone sequence

249

minimum theorem for continuous functions

250

minimum, local

251

minus (for sets)

252

monotone decreasing sequence

253

monotone function

254

monotone functions and discontinuities

255

monotone increasing sequence

256

monotone sequence

257

monotone sequences and convergence

258

monotonicity, derivatives, and local extrema

259

multiplication of Taylor series

260

n-th root sequence

261

neighborhood

262

nested compact sets

263

no square root (in Q)

264

non-measurable set

265

norm, supremum

266

nowhere differentiable function

267

one-sided limit

268

one-sided limits and limits

269

one-to-one

270

onto

271

open

272

open cover

273

open set, characterization

274

open set, inverse image under continuous function

275

open sets, intersections of

276

open sets, unions of

277

order of summation

278

ordered pairs of integers

279

ordered set

280

ordering

281

oscillation and essential discontinuities

282

outer measure

283

outer measure of intervals

284

outer measure, properties

285

p-series test

286

partial fraction decomposition

287

partial ordering

288

partial sum

289

partition of an interval

290

Peano axioms

291

Peano, Giuseppe (1858-1932)

292

perfect set

293

perfect sets are uncountable

294

Pi is irrational

295

Pi, series approximation

296

Pinching Theorem

297

pointwise convergence

298

pointwise convergence defines function

299

pointwise vs uniform convergence

300

polynomial (fixed degree, integer coefficients

301

polynomial (integer coefficients)

302

power sequence

303

power series, definition

304

power series, differentiating

305

power series, integrating

306

power series, theorem

307

power set

308

power set, cardinality of

309

power set, examples

310

preimage

311

prime numbers

312

principle of induction (axiom)

313

principle of induction (theorem)

314

product of series (Cauchy Product)

315

product rule

316

projective space

317

proof by contradiction

318

proof by induction,

319

quotient rule