open sentence
C1/C2Formal, Technical, Academic
Definition
Meaning
A mathematical or logical statement containing at least one variable that becomes true or false when the variable is replaced by a specific value.
A linguistic phrase or statement that is incomplete and requires additional context, information, or a variable to be resolved. In education, a sentence fragment or mathematical expression designed for students to complete.
Linguistics
Semantic Notes
In mathematics and formal logic, it is a precise term. In general discourse, it can be used more loosely to describe an unfinished or conditional statement.
Dialectal Variation
British vs American Usage
Differences
Usage is identical in both varieties within technical contexts. In general education, 'number sentence' is sometimes preferred in UK primary contexts, while 'open sentence' is standard in US math education.
Connotations
Strongly associated with mathematics/logic education in both. Slightly more common in American pedagogical terminology.
Frequency
Low frequency in general language; high frequency in mathematics education and logic textbooks in both regions.
Vocabulary
Collocations
Grammar
Valency Patterns
OPEN SENTENCE + with + variable (e.g., an open sentence with one variable)OPEN SENTENCE + involving + variable (e.g., an open sentence involving x and y)Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “Leave the sentence open (figurative: to not conclude a discussion)”
Usage
Context Usage
Business
Virtually unused.
Academic
Core term in mathematics, logic, and linguistics for an expression containing free variables.
Everyday
Rarely used; might be understood as an unfinished thought or a sentence needing completion.
Technical
Precise term in formal logic, algebra, and math education.
Examples
By Part of Speech
verb
British English
- To begin, you'll need to open the sentence with a variable.
- The exercise asks pupils to open the number sentence by replacing the box with 'n'.
American English
- First, open the sentence by inserting a placeholder.
- The teacher instructed us to open the math sentence using a letter.
adjective
British English
- The open-sentence format is common in primary maths textbooks.
- We were working on open-sentence problems.
American English
- The open-sentence exercise was challenging.
- He presented an open-sentence approach to algebra.
Examples
By CEFR Level
- The box in '3 + __ = 7' makes it an open sentence.
- Can you finish this open sentence? The cat is __.
- In algebra, 'y - 2 = 8' is an example of an open sentence.
- An open sentence is not true or false until you substitute a number for the variable.
- The truth set of an open sentence is the collection of values that make it a true statement.
- Logicians analyse open sentences to understand how quantifiers like 'for all' work.
- The predicate 'x is prime' constitutes an open sentence which becomes a proposition when x is instantiated.
- His argument relied on leaving a key premise as an intentionally open sentence to be interpreted by the reader.
Learning
Memory Aids
Mnemonic
Think of a sentence with an 'open' slot, like a blank (__) in a maths problem: 'x + 5 = 9' is open until you fill the blank with 4.
Conceptual Metaphor
A SENTENCE IS A CONTAINER (that can be open or closed). KNOWING IS FILLING A CONTAINER.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid translating as 'открытое предложение' in general contexts, as this more commonly means 'open offer/ proposal'. In maths, 'высказывательная форма' or 'предикат' is more accurate.
- Direct translation may lead to confusion with the grammatical concept of an 'unfinished sentence' ('незаконченное предложение').
Common Mistakes
- Using 'open sentence' to mean simply a long or complex sentence. Confusing it with a 'run-on sentence'. Using it outside of a mathematical or logical context without explanation.
Practice
Quiz
In which field is the term 'open sentence' most precisely defined?
FAQ
Frequently Asked Questions
No. A question is interrogative. An open sentence is declarative in form but contains a variable, making its truth value undetermined until the variable is specified.
Yes. An open sentence can contain one or more variables, e.g., 'x + y = 10'.
In a general, non-technical sense, yes—it's an incomplete statement requiring a noun. In strict mathematical logic, variables are typically symbols for numbers or objects, not words.
A closed sentence or a statement: a declarative sentence that is definitively true or false, with no variables requiring substitution, e.g., '7 + 5 = 12'.