In the spirit of the Paris-Harrington theorem, I would in fact expect some cases of Theorem 2 to undecidable statements of Peano arithmetic, although I do not have a rigorous proof of this assertion. Despite the complicated finitary interpretation of this theorem, I was still interested in ...
In the spirit of the Paris-Harrington theorem, I would in fact expect some cases of Theorem 2 to undecidable statements of Peano arithmetic, although I do not have a rigorous proof of this assertion. Despite the complicated finitary interpretation of this theorem, I was still interested in ...
In 2016, Illinois initiated a statewide transitional math program to support students to be academically ready in college-level math before graduating from
This is a crucial idea in general, for all GMAT probability questions, and one that will be very important in solving “at least” questions in particular. The complement of “at least” statements Suppose eventAis a statement involving words “at least”—how would we state what constituted ...
Because we’ve ignored latitude (see previous footnote), these statements are not literally true: they apply rather to the planet’s longitude compared with the Sun’s.For an outer planet, apogee occurs at conjunction and perigee at opposition. For an inner planet, apogee occurs at superior ...
The level of detail required to be convincing depends on the amount of mathematical knowledge the reader and the writer share. There is no need to translate those arguments into formal statements in predicate logic. In fact, that is usually a bad idea since it can obscure the mathematical mean...
THis digital activity includes 12 complete proofs: 9 drag & drop proofs for students to drag moveable statements or reasons into the proofs provided & 3 proofs where students type in each statement and reason. Proofs can be tricky for Geometry students, but practice CAN be engaging! 12 ...
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In geometry we’re learning about the correspondence of congruence statements (i.e. ∆ABC ≅ ∆DEF means that A maps to D, BC = EF, angle CAB ≅ angle FDE, etc). One fun type of problem you can do with this is a self-referential congruence statement to highlight symmetry. For...
Proving Statements About All Natural Numbers Induction comes in many flavors, but the goal never changes. We use induction when we want to prove something is true about all natural numbers. These statements will look something like this: For all natural numbers n, 1+2+⋯+n=n(n+1)/2. ...