Transfinite in a sentence
Synonym: infinite, immeasurable. Antonym: finite
Meaning: Relating to a quantity that is greater than any finite number.
(1) The aleph-null symbol is used in the study of transfinite numbers.
(2) The transfinite set theory revolutionized the field of mathematics.
(3) Transfinite numbers are used to describe the size of infinite sets.
(4) The transfinite cardinality of the set of natural numbers is aleph-null.
(5) Transfinite numbers can be used to describe the complexity of algorithms.
(6) The transfinite ordinal number omega is the smallest uncountable ordinal.
(7) The concept of transfinite numbers challenges our intuition about infinity.
(8) Transfinite set theory has implications for the foundations of mathematics.
(9) The concept of transfinite numbers has applications in theoretical physics.
(10) Transfinite calculus is used in the analysis of infinite series and limits.
Transfinite sentence
(11) The concept of transfinite recursion is used in computer science algorithms.
(12) The transfinite axiom of choice is a controversial assumption in set theory.
(13) The transfinite hierarchy of sets is a way of organizing sets by their size.
(14) Transfinite set theory provides a framework for analyzing infinite processes.
(15) Cantor's work on transfinite numbers laid the foundation for modern set theory.
(16) Cantor's diagonal argument is a key proof technique in transfinite mathematics.
(17) Transfinite induction is a fundamental principle in the study of infinite sets.
(18) The concept of transfinite numbers was introduced by mathematician Georg Cantor.
(19) The transfinite continuum hypothesis is a famous unsolved problem in mathematics.
(20) Transfinite set theory allows us to reason about infinite collections of objects.
Transfinite make sentence
(21) The study of transfinite cardinals and ordinals is a complex branch of mathematics.
(22) Understanding transfinite sets requires a deep understanding of mathematical logic.
(23) Transfinite induction is a powerful tool for proving statements about infinite sets.
(24) The concept of transfinite ordinals allows us to compare the sizes of infinite sets.
(25) The study of transfinite numbers has led to new insights into the nature of infinity.
(26) The transfinite continuum hypothesis is a conjecture about the size of the continuum.
(27) Transfinite arithmetic is used in computer simulations involving infinite populations.
(28) The concept of transfinite numbers has applications in cryptography and data security.
(29) Transfinite set theory has applications in various branches of science and engineering.
(30) The study of transfinite numbers has deep connections to the philosophy of mathematics.
Sentence of transfinite
(31) The study of transfinite numbers has led to important discoveries in mathematical logic.
(32) The study of transfinite mathematics has led to many important discoveries in set theory.
(33) Transfinite recursion is a powerful technique for solving problems with infinite solutions.
(34) The concept of transfinite numbers was introduced by Georg Cantor in the late 19th century.
(35) The transfinite continuum hypothesis has implications for the structure of the real numbers.
(36) The wellordering theorem is a key result in the theory of ordinals and transfinite induction.
(37) Transfinite sets are sets that are larger than any finite set but smaller than the set of all real numbers.
(38) The transfinite arithmetic of cardinal numbers is a powerful tool for studying the properties of infinite sets.
(39) The transfinite numbers are a fascinating topic in mathematics that has captured the imagination of many mathematicians.
(40) The transfinite recursion theorem is a fundamental result in set theory that allows for the construction of certain types of sets.
Transfinite meaning
Transfinite is an intriguing word that originates from the field of mathematics, specifically set theory. Coined by the German mathematician Georg Cantor in the late 19th century, it refers to a concept that extends beyond the realm of infinity. In this article, we will explore various tips on how to use the word "transfinite" or the phrase "transfinite set" in a sentence effectively.
1. Understand the meaning: Before incorporating the word "transfinite" into your sentence, it is crucial to grasp its definition. Transfinite refers to a quantity or concept that surpasses the infinite. It denotes a set or number that is larger than any finite number but not necessarily infinite. Familiarize yourself with this meaning to ensure accurate usage.
2. Contextualize the word: To use "transfinite" effectively, it is essential to provide context within your sentence. Consider the subject matter or topic you are discussing and determine if the concept of transfinite sets or numbers is relevant. By providing context, you will enhance the clarity and coherence of your sentence. Example sentence: "In the realm of mathematics, transfinite sets play a crucial role in understanding the concept of infinity and its various levels."
3. Use it in technical discussions: The term "transfinite" is commonly employed in technical discussions, particularly within the field of mathematics. If you are engaging in a conversation or writing an article related to set theory, topology, or mathematical logic, incorporating "transfinite" can demonstrate your understanding and expertise in the subject matter. Example sentence: "The study of transfinite numbers allows mathematicians to explore the boundaries of infinity and develop new mathematical frameworks."
4. Employ it in philosophical or abstract contexts: Transfinite can also be used in philosophical or abstract contexts to convey the idea of surpassing conventional limits or boundaries. When discussing abstract concepts, such as time, space, or the human mind, incorporating "transfinite" can add depth and complexity to your sentence. Example sentence: "The artist's work transcends the transfinite boundaries of imagination, evoking emotions that resonate with the depths of the human soul."
5. Utilize it in scientific or technological contexts: The concept of transfinite sets can also find application in scientific or technological discussions. When discussing topics such as computer science, artificial intelligence, or quantum mechanics, incorporating "transfinite" can highlight the cutting-edge nature of the subject matter. Example sentence: "Quantum computing harnesses the power of transfinite calculations, enabling complex computations that were previously unimaginable."
6. Consider the audience: When using the word "transfinite" or the phrase "transfinite set" in a sentence, it is crucial to consider your audience's familiarity with mathematical terminology. If you are addressing a general audience, ensure that your sentence provides sufficient context and explanation to aid comprehension. Example sentence: "The concept of transfinite sets, which extend beyond traditional notions of infinity, challenges our understanding of numbers and their infinite nature."
In conclusion, the word "transfinite" and the phrase "transfinite set" can be effectively incorporated into sentences by understanding their meaning, providing context, and considering the audience. Whether in technical discussions, philosophical contexts, or scientific explorations, the usage of "transfinite" can enhance the clarity and depth of your writing or conversation.
The word usage examples above have been gathered from various sources to reflect current and historical usage of the word Transfinite. They do not represent the opinions of TranslateEN.com.