Theorems · Theorem · special functions
Real.tendsto_exp_atTop
Filter.Tendsto Real.exp Filter.atTop Filter.atTop
The real exponential function tends to +∞ at +∞.
- Defined in
- Mathlib.Analysis.SpecialFunctions.Exp
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.Eventuallyproof · cited by 3,134
- Filter.atTopstatement and proof · cited by 2,405
- Real.expstatement and proof · cited by 871
- Filter.tendsto_idproof · cited by 180
- Filter.eventually_atTopproof · cited by 112
- Filter.tendsto_atTop_add_const_rightproof · cited by 20
- Filter.tendsto_atTop_mono'proof · cited by 17
- Real.add_one_le_expproof · cited by 13
Cited by10
Results whose statement or proof uses this declaration.
- summable_jacobiTheta₂_term_iffproof · cited by 4
- PhragmenLindelof.horizontal_stripproof · cited by 3
- Real.tendsto_exp_neg_atTop_nhds_zeroproof · cited by 2
- Real.image_exp_Ioiproof · cited by 2
- Complex.IsExpCmpFilter.isLittleO_im_pow_exp_reproof · cited by 1
- tendsto_rpow_atBot_of_base_lt_oneproof · cited by 1
- Real.tendsto_mul_exp_add_div_pow_atTopproof · cited by 1
- Real.image_exp_Iciproof · cited by 0
- Real.isBoundedUnder_le_exp_compproof · cited by 0
- tendsto_rpow_atTop_of_base_gt_oneproof · cited by 0