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Jan
23
revised When an equation has no solutions, denote it with $x\in\varnothing$.
added 388 characters in body
Jan
22
awarded  Peer Pressure
Jan
22
comment When an equation has no solutions, denote it with $x\in\varnothing$.
chat.stackexchange.com/rooms/20486/…
Jan
22
comment When an equation has no solutions, denote it with $x\in\varnothing$.
Do you agree it is an "unknown"?
Jan
22
comment When an equation has no solutions, denote it with $x\in\varnothing$.
When they say that "a variable is a mathematical object" they mean that it is an object used in mathematics to represent one or more numbers. If no numbers exist for it to represent, then the set it represents is empty. The variable does not exist in the set. The numbers it represents exist in the set. A variable is a symbol used to represent one or more numbers. Those numbers are in a set. Not the variable itself, it is just a letter.
Jan
22
comment When an equation has no solutions, denote it with $x\in\varnothing$.
First of all $x$ is not automatically something - a variable denotes an "unknown thing" we don't know whether anything exists in the solution set. The solution set here does not contain a variable. The solution set contains values of the variable that make the equation a true statement.
Jan
22
comment When an equation has no solutions, denote it with $x\in\varnothing$.
Okay, let's use $0\cdot x = 0$ instead :-)
Jan
22
comment When an equation has no solutions, denote it with $x\in\varnothing$.
recall: unknown quantities can be represented by words such as 'thing', etc. Also, drawings of squares etc. can be used to symbolize unknowns, and finally a letter, such as "x", can represent an unknown. In this case the "unknown quantities" has no value, therefore our our symbol that represents it can have no value. The other extreme is found in the case of the solution set of $x = 0/0$ over the set of real numbers; the solution set for x is the set of all real numbers that is to say x belongs to the set of all real numbers.
Jan
22
comment When an equation has no solutions, denote it with $x\in\varnothing$.
Okay, $x$ is 'something', or simply a 'thing'. Now, what that 'thing' is depends completely on what value make the equation a true statement. Since no value makes the equation a true statement the "thing" can have no value. The same argument is used when considering the solution set of $x=1/0$ over the set of real numbers; the solution set for x is the empty set that is to say x belongs to the empty set.
Jan
8
awarded  Quorum
Jan
7
awarded  Enthusiast
Jan
5
comment How to stop forgetting proofs - for a first course in Real Analysis?
The best way to stop forgetting is to only remember the analogies between the proofs.
Dec
31
revised Is $0$ an Infinitesimal?
added 148 characters in body
Dec
31
revised Is $0$ an Infinitesimal?
added 61 characters in body
Dec
31
answered Is $0$ an Infinitesimal?
Dec
23
comment What is the Scientific Notation of Zero?
Thank you for your detailed answer.
Dec
23
comment What is the Scientific Notation of Zero?
@JMoravitz And I thank you very much for all of that information :-)
Dec
23
accepted What is the Scientific Notation of Zero?
Dec
21
comment What is some pure math news website by a publisher?
As a subject becomes more advanced the level of technical abstraction increases.
Dec
21
comment What is some pure math news website by a publisher?
Current pure math achievements are not accessible to the average/common reader.