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Take agreeing sides for the two-sided limit where the expression is real on both - #2336
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Rafael-SOWNet merged 1 commit intoNov 2, 2026
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…eal on both Under the complex codomain, the default, two one-sided limits that agree were not taken for the two-sided one: x^x has a limit from the left only through its complex values, and no two-sided limit over the reals. (x^2)^x is real on both sides of 0 and tends to 1 from each, and its two-sided limit was NaN, the claim that there is none. They are now taken for it where the expression is real on both sides, decided structurally: every power to an exponent that is not whole, and every logarithm, has a base positive on both sides by SignNear. x^x is still NaN at 0. | | 2.6.0 and master | now | |---|---|---| | (x^2)^x at 0 | NaN | 1 | | (x*x)^(x - 1) at 0 | NaN | +oo | limitcheck, 600 expressions at each of seeds 1, 7 and 11: the findings are master's but for the (x*x)^(x - 1) row at seed 11, which is gone. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Codecov Report❌ Patch coverage is
Additional details and impacted files@@ Coverage Diff @@
## master #2336 +/- ##
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+ Coverage 86.76% 86.77% +0.01%
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Files 312 312
Lines 68526 68547 +21
Branches 19935 19946 +11
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+ Hits 59458 59485 +27
+ Misses 4907 4902 -5
+ Partials 4161 4160 -1
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Rafael-SOWNet
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November 2, 2026 20:27
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Found by limitcheck at seed 11. No issue was filed.
Under the complex codomain, which is the default, two one-sided limits that agree were not taken for the two-sided one. That rule exists for
x^x, which has a limit from the left only through its complex values and no two-sided limit over the reals (LimitTest.TestNoLimitpins this). But it also caught expressions that are real on both sides:(x^2)^xat 0NaN1(x*x)^(x - 1)at 0NaN+oox^xat 0NaNNaNNaNsays the limit does not exist, and each side is 1 (or+oo).Agreeing sides are now taken for the two-sided limit where the expression is real on both sides of the point. That is decided structurally: every power to an exponent that is not whole, and every logarithm, must have a base that is positive on both sides, by
SignNear. Anything not listed counts as not real, which costs coverage, never correctness.limitcheck, 600 expressions at each of seeds 1, 7 and 11: the findings and counts are master's, except at seed 11, where the
(x*x)^(x - 1)row is gone.Tests: the three cases in
ALimitRealOnBothSidesTestfail on master; the two controls,x^xand(x/pi)^x, pass on both. There is a BREAKING entry, A two-sided limit of an expression real on both sides is where its sides agree.🤖 Generated with Claude Code