Background for axioms
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axioms

/ˈæksiəmz/ /ˈæksiːəmz/

Meanings
noun
A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.

Examples :

"In geometry class, we started by accepting certain statements as axioms, like "a straight line is the shortest distance between two points," without needing to prove them. "
theory philosophy logic science statement math
noun
(proof theory) A fundamental assumption that serves as a basis for deduction of theorems; a postulate (sometimes distinguished from postulates as being universally applicable, whereas postulates are particular to a certain science or context).

Examples :

"In geometry class, students learn that all proofs start with fundamental truths called axioms, like the statement that a straight line can be drawn between any two points. "
theory math philosophy logic science

Related Words

Illustration assumption

assumption noun

/əˈsʌmp.ʃən/

The act of assuming, or taking to or upon oneself; the act of taking up or adopting.

"His assumption of secretarial duties was timely."

Illustration considered

considered verb

/kənˈsɪdəd/ /kənˈsɪdɚd/

To think about seriously.

"Consider that we’ve had three major events and the year has hardly begun."

Illustration fundamental

fundamental noun

/ˌfʌndəˈmɛntəl/

(usually in the plural) A leading or primary principle, rule, law, or article, which serves as the groundwork of a system; an essential part

"one of the fundamentals of linear algebra"

Illustration particular

particular noun

/pəˈtɪkjələ/ /pəˈtɪkjəlɚ/

A small individual part of something larger; a detail, a point.

"The teacher pointed out a particular detail in the math problem that several students missed. "

Illustration postulates

postulates noun

/ˈpɑstʃəleɪts/ /ˈpɑstjəleɪts/

Something assumed without proof as being self-evident or generally accepted, especially when used as a basis for an argument. Sometimes distinguished from axioms as being relevant to a particular science or context, rather than universally true, and following from other axioms rather than being an absolute assumption.

"In geometry class, one of the initial postulates is that a straight line can be drawn between any two points; this allows us to build more complex shapes and theorems. "

Illustration proposition

proposition noun

/ˌpɹɑpəˈzɪʃən/

The act of offering (an idea) for consideration.

"My teacher made a proposition for a new class project: a school-wide recycling drive. "

Illustration seemingly

seemingly adverb

/ˈsiːmɪŋli/

As it appears; apparently.

"The dog seemed happy, seemingly wagging its tail excitedly. "

Illustration statements

statements noun

/ˈsteɪt.mənts/

A declaration or remark.

"The teacher asked us to write statements about what we learned in class today. "

Illustration distinguished

distinguished verb

/dɪsˈtɪŋɡwɪʃt/

To recognize someone or something as different from others based on its characteristics.

"The teacher distinguished the students' excellent essays from the others based on their insightful analysis. "

Illustration applicable

applicable adjective

/əˈplɪkəbəl/

Suitable for application, relevant

"The new rule about late submissions is applicable to all students in the class. "

Illustration established

established verb

/ɪˈstæb.lɪʃt/

To make stable or firm; to confirm.

"The company established a new policy to improve employee safety. "

Illustration universally

universally adverb

/ˌjuːnɪˈvɜːsəli/ /ˌjunɪˈvɝsəli/

In a universal manner.

"The new school uniform is universally popular with the students. "