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Theorems · Definition · order theory

Complex.partialOrder

PartialOrder ℂ

We put a partial order on ℂ so that z ≤ w exactly if w - z is real and nonnegative. Complex numbers with different imaginary parts are incomparable.

Defined in
Mathlib.Analysis.Complex.Order
Cited by
64 results in Mathlib
Foundations
Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
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PositiveLinearMap.PreGNS · cited by 10PositiveLinearMap.PreGNSPositiveLinearMap.ofPreGNS · cited by 8PositiveLinearMap.ofPreGNSPositiveLinearMap.toPreGNS · cited by 5PositiveLinearMap.toPreGNSComplex.le_def · cited by 5Complex.le_defPositiveLinearMap.leftMulMapPreGNS · cited by 4PositiveLinearMap.leftMul…Mathlib.Meta.Positivity.ofReal_pos · cited by 4Positivity.ofReal_posLSeries.positive · cited by 3LSeries.positiveComplex.lt_def · cited by 3Complex.lt_defComplex.inv_natCast_cpow_ofReal_pos · cited by 3Complex.inv_natCast_cpow_…Complex.nonneg_iff · cited by 3Complex.nonneg_iffPositiveLinearMap.GNS · cited by 3PositiveLinearMap.GNSPositiveLinearMap.gnsNonUnitalStarAlgHom · cited by 3PositiveLinearMap.gnsNonU…PositiveLinearMap.leftMulMapPreGNS_apply · cited by 2PositiveLinearMap.leftMul…Complex.zero_lt_real · cited by 2Complex.zero_lt_realLSeries.iteratedDeriv_alternating · cited by 2LSeries.iteratedDeriv_alt…PartialOrder · cited by 6410PartialOrderComplex · cited by 5565ComplexComplex.partialOrderCITED BYCITES

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Cited by72

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