It follows that

How it is used

A more formal alternative to 'so'. Similar linking words in mathematical writing are 'hence', 'therefore', 'thus' and 'consequently'. Use 'it follows from A that B' when you want to name the reason.

Example sentences

1. Since x² = 9 and x is positive, it follows that x = 3.

2. It follows from Lemma 2 that the function is increasing.

Common collocations

• it follows that
• it follows from
• it then follows that
• hence
• therefore

Related terms

• proofA logical argument that shows, step by step from accepted facts, that a mathematical statement is always true.
• let x beA fixed phrase used to introduce a variable or an assumption at the start of a solution or proof, as in 'Let x be the number of tickets sold'.
• QEDShort for the Latin 'quod erat demonstrandum', meaning 'which was to be shown'; written at the end of a proof to show that it is complete.
• if and only ifA phrase joining two statements that are either both true or both false, so that each one implies the other; written ⇔ or 'iff'.

More terms: Proofs and Mathematical Writing

• theorem
• counterexample
• lemma
• proof by contradiction
• proof by induction
• without loss of generality