Express the interval form (- 0.5, 0.5) in modulus form.

1.	Express the interval form (- 0.5, 0.5) in modulus form.
Answer» Interval form: {- 0.5, 0.5) ∴ a – δ = – 0.5, a + δ = 0.5 By adding, 2a = 0 ∴ a = 0 Putting a = 0 in a + δ, δ = 0.5 In modulus form: \|x – a\| < δ ∴ For (- 0.5, 0.5), modulus form is expressed by \|x – 0\| < 0.5 = \|x\| < 0.5

Answer»

Interval form: {- 0.5, 0.5)

∴ a – δ = – 0.5, a + δ = 0.5

By adding, 2a = 0 ∴ a = 0

Putting a = 0 in a + δ, δ = 0.5

In modulus form: |x – a| < δ

∴ For (- 0.5, 0.5), modulus form is expressed by

|x – 0| < 0.5 = |x| < 0.5

Discussion