Quick question about infinity symbol

[zeion]

Homework Statement

Is it bad to put something like 0 < x < (inf) ?
Since infinity is not a number.

Homework Equations

The Attempt at a Solution

 

[mharten1]

Homework Statement

Is it bad to put something like 0 < x < (inf) ?
Since infinity is not a number.

Homework Equations

The Attempt at a Solution

What do you mean, "is it bad?" Do you mean to ask if it's allowable? Of course; in pre-calculus, when defining the domain and/or range of a function, many times you will use infinity.

For example, the domain of a simple function f(x)=x² would be -∞ < x < ∞ . Of course, this means the same thing as all real numbers (ℝ). However, it is definitely allowable to use infinity.

 

[zeion]

What do you mean, "is it bad?" Do you mean to ask if it's allowable? Of course; in pre-calculus, when defining the domain and/or range of a function, many times you will use infinity.

For example, the domain of a simple function f(x)=x² would be -∞ < x < ∞ . Of course, this means the same thing as all real numbers (ℝ). However, it is definitely allowable to use infinity.

Okay, because I was used simply defining something like that as the set of real numbers. I meant to ask if it was bad form.

 

[mharten1]

Okay, because I was used simply defining something like that as the set of real numbers. I meant to ask if it was bad form.

You'll have to use infinity many times. Another example is a piecewise function:

f(x) = { x² if x ≥ 0

How would you define the domain of that function?

0 < x < ∞ or in interval notation, [0,∞).

Using infinity still defines a set of real numbers. It just defines ALL of the real numbers.