Every ring is a field.
Every vector space is finite dimensional.
Every group is a torsion monoid.
Every finite simple group has prime order.
Every finite group is simple.
Every finite group has prime order.
Every set has Lebesgue measure zero.
If a topological space is compact, then every subset is compact.
Every set that is Lebesgue measurable but not Borel measurable has Lebesgue measure zero.
A finitely-presented group containing a torsion element is finite.
If every point of a subset of a topological space is contained in some closed set, the subset itself is closed.
A topological space $X$ is Hausdorff if and only if the diagonal map is an open map from $X$ to $X × X$.
Any finite order element in a group is equal to the identity.
If a subgroup of a group is torsion-free, then the group itself is torsion free.
Every injective homomorphism from a finitely generated free group to itself is surjective.
Every division ring is either a field or finite.
Every natural number is the product of two primes.
Every even number is the square of a natural number.
Every normal subgroup of a group has finite index.
The characteristic polynomial of every matrix has real roots.
In a commutative ring, every prime ideal is contained in a unique maximal ideal.
Every continuous function is uniformly continuous.
Every uniformly continuous function is bounded above.
If every compact subset of a topological space is closed, then the space is compact.
In a commutative ring, the sum of idempotent elements is idempotent.
The number of partitions of a finite set is a prime number.
If a poset has a maximal element, then it has a unique minimal element.
The automorphism group of an Abelian group is cyclic.
If a function from the unit interval to itself has a fixed point, then it has points of all positive periods.
The complement of the union of two sets contains the union of their complements.
The square root of an rational number is rational.
If a module over a ring is free, then the ring is commutative.
If the set of units of a ring forms a group then the ring is commutative.
Every natural number larger than `10` is the sum of a square and a prime.
The initial object of a category is isomorphic to its terminal object.
If the composition of two functions is continuous, then each of them is continuous.
If `a` commutes with `b` and `b` commutes with `c` then `a` commutes with `c`.
If an element maps to zero under a ring homomorphism, then it is zero.
Implication `→` is symmetric. If `P → Q` then `Q → P`.
Two natural numbers are equal if and only if they are both divisible by some prime number.