Language of Proof (Edexcel A-Level Mathematics): Flashcards

Establishing truth through logical reasoning

Proven statements based on axioms or other theorems

Supporting theorems assisting in proving larger results

Consequences that directly follow from a theorem

Statements believed true but not yet proven

Applies to all elements in a set

At least one element satisfies the statement

Start from general principles and logically deduce

Consider all possible cases

Disprove with specific example where statement fails

Assume opposite, show this leads to contradiction

Natural numbers (positive integers $\geq 1$)

All integers (positive, negative, and zero)

Rational numbers ($\frac{a}{b}$, $a,b \in \mathbb{Z}$)

Intersection of sets (common elements)