Proving |xy-ab| is Less Than Epsilon: Absolute Value Question | Homework Help"

In summary, absolute value is a mathematical concept that measures the distance of a number from zero on a number line and is always positive. To find the absolute value of a number, the negative sign is removed. It is different from magnitude, which refers to the size or quantity of a number. There are several rules for absolute value, and it has various real-life applications in fields like physics, engineering, and economics.
  • #1
mercuryman
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0

Homework Statement



Given: |x-a|<ε |y-b|<ε. proove: |xy-ab|<ε(|a|+|b|+ε)


Homework Equations


I need a direction for this proof.


The Attempt at a Solution


I tried by the info: -ε+a<x<ε+a and -ε+b<y<ε+b to ,multiply these inequalities, but it's not true. and i tried with the opposite triangle inequality and it didn't worked.
 
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  • #2
You can expand |xy-ab| to contain terms like a(y-b) and then use the regular triangle inequality.
The direction multiplication of the inequalities could work, too, but you have to be careful with signs there.
 

Related to Proving |xy-ab| is Less Than Epsilon: Absolute Value Question | Homework Help"

What is absolute value?

Absolute value is a mathematical concept that refers to the distance of a number from zero on a number line. It is always a positive value, regardless of the sign of the number.

How do you find the absolute value of a number?

To find the absolute value of a number, you simply remove the negative sign (if present) and keep the positive value. For example, the absolute value of -5 is 5, and the absolute value of 10 is also 10.

What is the difference between absolute value and magnitude?

Absolute value and magnitude are often used interchangeably, but they have different meanings. Absolute value refers to the distance from zero on a number line, while magnitude refers to the size or quantity of a number.

What are the rules for absolute value?

There are a few rules for absolute value, including:

  • The absolute value of a positive number is the number itself.
  • The absolute value of a negative number is the positive version of that number.
  • The absolute value of zero is zero.
  • The absolute value of a product is equal to the product of the absolute values of the individual factors.
  • The absolute value of a quotient is equal to the quotient of the absolute values of the numerator and denominator.

How is absolute value used in real life?

Absolute value has many practical applications in real life, such as calculating distances, determining the difference between two values, and solving equations involving absolute value. It is also commonly used in fields such as physics, engineering, and economics.

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