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kathrynag
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Homework Statement
Show that if a | c and b | c, and (a, b) = d, then ab | cd.
Homework Equations
The Attempt at a Solution
Abstract divisibility.
We have c=am, c=bn, and d=an+bm.
Abstract divisibility is a concept in mathematics and logic that refers to the ability to divide an object or concept into smaller, more abstract parts. It can be applied to various fields such as set theory, algebra, and graph theory.
Regular divisibility is a concept in arithmetic that refers to the ability to divide a number into equal parts without a remainder. Abstract divisibility, on the other hand, involves dividing an object or concept into smaller, more abstract parts without necessarily involving numbers or quantities.
Some examples of abstract divisibility in the real world include dividing a country into states, dividing a computer program into functions, and dividing a book into chapters. In each of these cases, the larger object is divided into smaller, more abstract parts to make it more manageable or to better understand its structure.
Yes, abstract divisibility can be applied to various non-mathematical concepts such as language, music, and art. For example, a language can be divided into phonemes, words, and sentences, while a piece of music can be divided into notes, measures, and sections. In these cases, abstract divisibility helps to analyze and understand complex systems or structures.
Abstract divisibility is a valuable tool in scientific research as it allows scientists to break down complex systems or phenomena into smaller, more manageable parts. This makes it easier to study and analyze these systems and draw meaningful conclusions. Additionally, abstract divisibility can help identify patterns and connections between different abstract parts, leading to new discoveries and advancements in various fields of science.