This document defines key terminology used in mathematical proofs: 1. A statement is a sentence that is either true or false, and can be simple or composite. A hypothesis is a statement assumed to be true from which consequences follow. 2. A conclusion is a statement that follows from previously assumed conditions or hypotheses. A definition provides an unequivocal meaning for a word, phrase, or concept to avoid confusion. 3. A proof is a logical argument that establishes the truth of a statement beyond doubt using a chain of logical steps. A theorem is a statement given or implied by constructing a proof.

1. Name : 1. Arif Miswanto
2. Feralia Goretti Situmorang
3. Hanifa Zulfitri
4. Nadya Putri Setiawatu
TERMINOLOGY TASK
At the beginner’s level – the level for reader of this book – this feeling is often the result of
the use of an unproductive and often unsystematic ( and panicky ) approach that leads to
hours of unfruitful work. The construction of airtigh logical construction “proofs” represents
one of the major abstacles mathematical neophytes face when making the transition to more
advanced and abstract material. To learn how to read and understand proofs (this term will be
defined more precisely in the few paragraph) already written in a textbook, and to learn how
to construct proofs on our own, we will proced by breaking them down into a series of simple
steps and looking at the clues that lead from one step to the next. “Logic” is the key that will
help us in this process.
Statement : A statement is a sentence expressed in words (or mathematical symbols) that is
either true or false. A statement is simple when it can’t be broken down into other statements
(e.g., “it will rain”. “two plus two equals four”. “i like that book”). A statement is composite
when it is buit by using several simple statement connected by punctuation and/or word such
as and, although, or, thus, them, therefore, because, for, moreover, however, and so on (e.g.,
“a white horse is white”. “either you have a dollar bill or you don’t.”) is called a tautology.
On the other hand, a sentence whose truth can’t be established is called a paradox. A classic
example is goven by the sentence is false! If we decide that the sentence is false, then it is
false that the sentence is false. Thus the sentence must be true!
Hypothesis : A hypothesis is a statement that it is assumed to be true, and from ehich some
consequence followa. ( e.g., in the sentence “ if we work on this problem, we will understand
it better” the statement “we work on this problem” is the hypothesis). There are other
common uses of the work hypothesis in other scientific fields, ad they are considerably
different from the one listed here. For example, in mathematic hypotheses are never tested. In

2. other fields (e.g., statistic, biology, psychology) scientists discuss the need “to test the
hypothesis”.
Conclusion : A conclusion is a statement that follows as a consequences from previously
assumed conditions (hypothesis). (e.g., in the sentence “if we work on this problem, we will
understand is better” the statement “we will understand is better” is the conclusion).
Definition : A definition is an unequivocal statement of the precise meaning of a word or
phrase, a mathematical symbol or concept, to end all possible confusion.
Knowing and understanding definition will save a lot of time and frustration. This isn’t to
suggest that definitions should be memorized by rote, without understanding them. It is a
good idea to work with new definitions to be sure that their meanings and immediate
consequence are clear, so that it will be possible to recall them quickly and appropiately.
Therefore, we should make sure to have a good starting point by having a clear and thorough
understanding of all necessary deffinitions.
Proof : A proof is a logical argument that establishes the truth of ststement beyond any doubt.
A proof consists of a finite chain of steps, with each one of them being a logical consequence
of the previous one. Theorem : A theorem is a mathematical statement that are explicitly
given or implied in the statement (i.e., by constructing a proof). The word theorem shares its
Greek root with the work theater.
Lemma : A lemma is an auxiliary theorem proved beforehand, so that it can be used in the
proof of other theorem. This word comes from the Greek word that means “to grasp.” Indeed
in a lemma one “graphs” some truth to be used in the proof of a larger result. The proof of
some theorems are long and difficult to follow. Often the result stated in lemmas aren’t very
interesting by themselve, but they play key roles in the proof of more important result. On the
other hand, there are some lemmas that are used in so many different cases and are so
important that they are named after famous mathematicians. Corollary : A corollary is a
theorem that follows logically and easily from a theorem already proved. Corollary can be
important theorem.
GENERAL SUGGESTIONS
The first step, whether we are trying to prove a result in our own are trying to understand
someone else’s proof, consist of clearly understanding the assumptions made in the statement

3. of the theorem and the conclusion to be reached. In this way we are establishing that starting
and ending points of the logically process that will take us from the hypothesis so the
concusions. We must understand the meaning of the hypothesis so that we can use the full
strength of the information we are given, either implicitly or explicitly, to achive the desired
result. It is essential to check all technical words appearing, in the statement and to review the
definitions of the ones whose meaning aren’t clear and familiar.