High school
Evidence for f ≠ 0 and f = 0 cannot both hold for the same f.
“This same box contains zero sweets” and “this box contains a nonzero number of sweets” cannot both be true. Two different boxes with different amounts would cause no contradiction. The same object matters.
Think with the concrete example above. You can try again.
Two different boxes may hold different amounts. A contradiction requires incompatible statements about the same object under the same conditions.
Your answer fits this explanation. Look for the same idea in the comic.
No; the objects may differ. Two different boxes may hold different amounts. A contradiction requires incompatible statements about the same object under the same conditions.
One f cannot satisfy both f ≠ 0 and f = 0. A nonzero f and a different zero g would not be a contradiction.
FLT · aa2d8b3 · S_FreyPackage_no_frey_package.lean
hf (ModularForm.S2_Gamma0_2_eq_zero f)hf is the nonzero evidence; the argument supplied to it proves the same form is zero. The source shows the contradiction’s application, not a new axiom.
Contradiction with the same object
Read the three explanation steps first. The Lean source is there for a closer look afterwards; you do not have to read it first.
Evidence for f ≠ 0 and f = 0 cannot both hold for the same f.
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One f cannot satisfy both f ≠ 0 and f = 0. A nonzero f and a different zero g would not be a contradiction.
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