theorem - Master This Word
Master this word with our 5-step learning method – Learn English in English
theorem Word Meanings
- A statement that can be proven based on previously established statements.
- A principle or proposition in mathematics.
- A theory that has been demonstrated as true.
theorem Example Sentences
Example sentences are the start of understanding. Don't rush to memorize. First feel how the word works in a sentence.
theorem Phonetic & Pronunciation
UK
/ˈθɪərəm/
US
/ˈθɪrəm/
theorem Word Etymology
Root decomposition: 'theorein' (to see) + 'ema' (result); Historical origin: Greek → Latin 'theorema' → Old French 'theoreme' → English; Memory image: Imagine a mathematician unveiling a hidden equation, illuminating the dark with the light of understanding, as if revealing a secret treasure.
Note 1: These definitions and etymologies are not standard dictionary definitions, but extended explanations provided to help with memorization and understanding of the actual application of words. Through this background information, we strive to make words more vivid and easier to understand, and help you remember their meanings in real life.
Note 2: LexiTalk designs the learning flow around the linguistics principle of “Comprehensible Input.” When learners encounter material that is slightly above their level but still understandable from context, the brain naturally absorbs the language. That’s why we keep every word inside authentic contexts, using examples and associations to help you understand it and use it flexibly.
Read the FAQ explanation of Comprehensible InputReal Context
An established statement in mathematics that has a proof. A theorem is proven from axioms, definitions, and previously proven results, and is accepted as true within a given system. Theorems are not mere ideas; they come with a formal demonstration that can be checked step by step. In textbooks you will see numbering like Theorem 2.1 or named theorems such as the Pythagoras theorem, and the proof is essential, not optional. The word is contrasted with conjecture (unproven) and lemma (a helper result). For learners, the challenge is to grasp both the statement and the reasoning that leads to the proof, and to see how the theorem enables further conclusions.
Usage Reminders
- Know that a theorem has a proof.
- Differentiate theorem from conjecture and lemma.
- Pay attention to the exact hypotheses.
- Learn the proof structure, not only the conclusion.
- Practice referencing the theorem in new problems.
Common Misconceptions
- A theorem is just a guess.
- All theorems apply to every situation without checking hypotheses.
- A theorem is the same as a law.
- Proofs are optional and not important.
- Once you memorize a theorem, you understand it completely.
Thinking Differences
In English, the term theorem signals a rigorously proven statement within a formal mathematical discourse. Learners often mix it up with a law, a principle, or a conjecture. The emphasis is on proof structure and the exact hypotheses. Mistakes include treating theorems as universally applicable without checking context or confusing a lemma with a main theorem.
Learning Tips
- Read the statement carefully and identify the hypotheses.
- Study the proof structure, not just the conclusion.
- Work through a full, detailed proof once.
- Compare with a lemma to see how smaller results fit together.
- Practice applying the theorem to different problems.
- Explain the theorem in your own words to solidify understanding.
5-Step Learning Method - Learn English in English
Step 1: Meaning
What is the definition of 'theorem'?
A.A type of experiment conducted under controlled conditions.
B.An opinion or belief that is not based on facts.
C.A statement or proposition that can be proven based on previously established statements or propositions.
D.A method of cooking food.
Step 2: Usage
Identify the correct usage of the word 'theorem' in a sentence.
A.The theorem of cooking pasta perfectly involves boiling it for hours.
B.The theorem of relativity revolutionized our understanding of space.
C.According to the theorem, all triangles are square in shape.
D.The theorem proves that every action has an equal and opposite reaction.
Step 3: Similar Words
Which word is most similar to 'theorem'?
A.Postulate
B.Hypothesis
C.Proposal
D.Concept
Step 4: Opposite Words
What is the opposite of 'theorem'?
A.Hypothesis
B.Truth
C.Opinion
D.Fact
Step 5: Mastery
Can you think of a real-life context involving a theorem?
A.In physics, a new rule was discovered about how objects move in space.
B.One student proposed an idea for the science fair based on their observations.
C.In mathematics class, I learned about the Pythagorean theorem and how it applies to triangles.
D.Scientists concluded that their findings were just opinions in a discussion.
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