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May
7
comment What is the difference between the domain of a variable and the domain for an equation?
Equations, on the other hand, are said to have a solution set consisting of all the values of the variable(s) that turns the open sentence into a true statement, these are all the values that satisfy the sentence.
May
7
comment What is the difference between the domain of a variable and the domain for an equation?
A variable in an equation can be replaced by any of the numbers in the variable's domain. The resulting equation may be either true or false. Alternatively, replacing each variable in an open sentence by each of the values in the variable's domain is a way to find solutions of the open sentence. Here is another way to show that the domain of a variable y is {1, 2, 3, 4}: y $\in$ {1, 2, 3, 4} Read "y belongs to the set whose members are 1, 2, 3, and 4." Again alternatively, this could be read "What y can be replaced by belongs to the set whose members are 1, 2, 3, and 4."
Apr
27
comment role of definitions in proofs
Definitions do not, as you say, "define objects." Instead, as any dictionary shows, they define the words we use for objects. Where they come from would be a matter of accepted convention.
Apr
24
comment Could somebody please help me prove this using the properties of real numbers introduced in elementary algebra?
Is it logically correct to state "1 is its own reciprocal because 1 * 1 = 1." And to prove this by the identity property of multiplication: a * 1 = a? Given that we know, by definition, reciprocals are two numbers whose product is 1.
Apr
24
comment Is an empty parenthesis a valid mathematical expression?
Short answer: no.
Apr
24
comment Could somebody please help me prove this using the properties of real numbers introduced in elementary algebra?
In the equation 1/1 = 1 the right hand side is called a fraction in simplest form. Does that mean all the integers are fractions in simplest form? But a ratio in simplest form must be n/1 for n = integer?
Apr
20
comment Finding all possible pairs of positive integer values
But, if x is equal to y the ratio is undefined.
Apr
20
comment Finding all possible pairs of positive integer values
Why do you put the "equal to" into your condition: Assume x >= y?
Apr
16
comment How would multiplying money work?
But if that meal has a negative nutritional value "imagine" the complexities ;-)
Feb
20
comment A set without the empty set
Sometimes textbooks tell the reader that the symbol $\in$ is read "belongs to", how does anything belong to the empty set?
Oct
20
comment Couple Probability
@BrianM.Scott welcome back from skullpatrol, now known as Ice Boy, and the rest of the gang in the chatroom :-)
Sep
26
comment How do you read the symbol “$\in$”?
Would these two different roles of a variable be more clearly shown in the phrases: "any value of the variable in its domain" versus "the specific, but as of yet unknown, value of the variable"?
Sep
26
comment “Negative” versus “Minus”
clap, clap, clap
Sep
19
comment How do you read the symbol “$\in$”?
Thank you for the helpful links.
Sep
19
comment High school math definition of a variable: the first step from the concrete into the abstract…
Thank you for your answer(s). How is this question related to your answer here?
Sep
18
comment How do you read the symbol “$\in$”?
Ho Hey
Jul
25
comment How find this limit $I=\lim_{n\to\infty}n^a\left(\int_{0}^{\pi/2}\sin{(nx)}\cos^n{x}dx\right)=b$
Please come back @Chris'ssis
Jul
3
comment Trying to explain what “consistent” means to a middle schooler
@DaveL.Renfro what would be the first math thing you would use?
Jun
29
comment Trying to explain what “consistent” means to a middle schooler
Thank you for the clear explanation, but how can this be shown at the elementary Algebra level studied in middle school at the age of 13 years old?
May
3
comment What is the difference between equation and formula?
Note: Not every equation is a formula; but by the above definitions, every formula must be an equation in algebra.