to find a clear solution; to come to a clean decision; to give a clear explanation; to divide exactly (without remainder); to divide evenly
numerator; molecule; member; element
prime factorization; prime decomposition
to form a pair; to pair up
participation; taking part in; participating in; being concerned in
indicates position in a sequence; divisions of a kabuki performance
to take (a resource, e.g. time or money); to hang; to come into view; to arrive; to come under (a contract, a tax); to start (engines, motors); to attend
showing by a diagram; illustrating; representing graphically
please; somehow or other; one way or another
exemplification; illustrating by example
mathematical principle; mathematics; arithmetic; figures; accounts
continuation; succession; series
claim; insistence; assertion; advocacy; emphasis; contention
suitable; proper; appropriate; perfunctory; half-minded; sloppy
so; therefore; accordingly; like I said; I told you already
previous time; last time; previous installment; previous instalment; previous session
because of; on account of; regarding; per; apiece
induction; inductive reasoning
hypothesis; supposition; assumption; tentative theory
previously; before; first; before (something or someone else); beforehand; in advance
stochastic; probabilistic
from time immemorial; ancient; time-honoured; time-honored
attraction; fascination; lure; captivation; charm
smallness; small item; short month (i.e. having fewer than 31 days); elementary school; smaller (of two things, places, etc. with the same name); inferior; younger (of two people with the same name)
combination; union; incorporation; congruence
certain; sure; definite; reliable; sound; solid
probability; likelihood; chances
both ends; either end; both edges; double-mindedness; sitting on the fence
all; whole; entire; complete (set); in total