Indefinite Numbers In Math

Previously we first understand zero, left approach, right approach, and infinite number.

Zero Definition

Zero is a number representing the number of empty set elements, in short:

n (Ø) = 0

For example:
A = {People whose height is 10 meters}, n(A) = 0
B = {The Jakarta man whose wife is 1000}, n(B) = 0

Number x ∈ real:

1. x → 0_- or 0^- or x ↑ 0, meaning that the number x is close to 0 from left / bottom / negative.
   x → 0₊ or 0⁺ or x ↓ 0, meaning that the number x is close to 0 from right / up / positive.
2. x → ∞ or x ↑ ∞, meaning that  x to infinity or x rise infinitely.
   x → -∞ or x ↓ -∞, meaning that x to infinity or x rise infinity.

The properties of the numbers 0, 1, and ∞ are as follows:
a/0+ = ∞, a > 0
a/0_- = -∞, a > 0
a/0+ = -∞, a < 0
a/0_- = ∞, a < 0
0/a = 0, a ≠ 0
0 x a  = 0, a ≠ + ∞
0^∞ = 0
0^-∞ = ∞
a/0 = ∞, a > 0
a/0 = -∞, a < 0
1^a = 1, a ≠ + ∞
0^a = 0, a > 0
0^a = ∞, a < 0
a⁰ = 1, a ≠ 0
a⁰ = 1, a ≠ + ∞
a^∞ = ∞, a > 1
a^∞ = 0, 0 < a < 1

So 0/0, ∞/∞, ∞ - ∞, 0.∞, 0⁰, ∞⁰, 1^∞ are called indefinite numbers.

Uncertain numbers usually appear on limit issues. Said not necessarily, because given the results of any true. The number is raised because it is often confused between a certain number and not certain on the count operation for the numbers 0, 1, and ∞.

A few articles this time. Sorry if there is a wrong word.

The end of word wassalamualiakum wr. wb.

Reference:

• Calculus Book (WIKARIA GAZALI SOEDADYATMODJO)

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