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revised A ring that is not a Euclidean domain
Revert yet another incorrect edit by another user
Feb
4
revised A ring that is not a Euclidean domain
revert incorrect edit by another user
Jan
26
awarded  Good Answer
Jan
23
awarded  Good Answer
Jan
8
awarded  Enlightened
Jan
7
awarded  Nice Answer
Jan
5
awarded  Great Answer
Dec
31
revised How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
added 1217 characters in body
Dec
31
revised Why is sum of a sequence $\displaystyle s_n = \frac{n}{2}(a_1+a_n)$?
fix link rot due to despicable deletions
Dec
29
awarded  Guru
Dec
29
awarded  Good Answer
Dec
26
comment Why do we do mathematical induction only for positive whole numbers?
Look up structural induction for a more general perspective on where it works.
Dec
18
answered Why aren't there any solutions?
Dec
15
comment Does “Doing a thing to both sides of an equation” have a name?
@Pedro Yes, the edit certainly helps to clarify. Unfortunately there is no standard name used for this property in elementary contexts (that's the first I've heard of Suppes' name for it). But there is now enough information in the answers and comments that anyone who desires to learn more should have a good starting point. Thanks for keeping an open mind.
Dec
14
awarded  Announcer
Dec
13
comment Does “Doing a thing to both sides of an equation” have a name?
@Pedro I said nothing about a "specific operation involved". Rather, what is specific is the property that the OP seeks a name for, i.e. equations being preserved by "doing a thing to both sides". This is a specific law - distinct from many other named algebraic laws (e.g. associative, commutative, distributive, etc) that are all part of "doing algebra".
Dec
13
comment Does “Doing a thing to both sides of an equation” have a name?
@Pedro The OP asks for a generic name for the given property, not for every algebraic property known.
Dec
13
comment Does “Doing a thing to both sides of an equation” have a name?
@ToddWilcox Please see my prior recent comments.
Dec
13
comment Does “Doing a thing to both sides of an equation” have a name?
The linked article should do a better job of stressing the key point that this property holds because we are substituting/replacing an argument by an equal value in a mathematical (set-theoretic) function. For more general "functions" it may fail, e.g. in computer science, for programming functions - see pure function, deterministic algorithm, referential transparency.
Dec
13
comment Does “Doing a thing to both sides of an equation” have a name?
@ColinK This property of mathematical functions has more widely-used names in more general contexts where it may fail for various reasons, e.g. in computer science, for programming functions, e.g. see pure function, deterministic algorithm, referential transparency. See also my comments here.