Real Numbers and Sequences
Completeness, suprema, sequence convergence, and Bolzano-Weierstrass.
Reference Irreducible Polynomials over the Integers versus over the Real Numbers
This reference explains why irreducibility depends on the coefficient system you allow in a factorization. For Grade 10 factoring and early university algebra, the key idea is that a polynomial can be irreducible in Z[x] but reducible in R[x], because the real numbers allow factors with irrational coefficients.