1 Additive Inverse :
The additive inverse of 1 is -1.
This means that when we add 1 and -1, the result is zero:
1 + (-1) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 1
- Additive inverse: -1
To verify: 1 + (-1) = 0
Extended Mathematical Exploration of 1
Let's explore various mathematical operations and concepts related to 1 and its additive inverse -1.
Basic Operations and Properties
- Square of 1: 1
- Cube of 1: 1
- Square root of |1|: 1
- Reciprocal of 1: 1
- Double of 1: 2
- Half of 1: 0.5
- Absolute value of 1: 1
Trigonometric Functions
- Sine of 1: 0.8414709848079
- Cosine of 1: 0.54030230586814
- Tangent of 1: 1.5574077246549
Exponential and Logarithmic Functions
- e^1: 2.718281828459
- Natural log of 1: 0
Floor and Ceiling Functions
- Floor of 1: 1
- Ceiling of 1: 1
Interesting Properties and Relationships
- The sum of 1 and its additive inverse (-1) is always 0.
- The product of 1 and its additive inverse is: -1
- The average of 1 and its additive inverse is always 0.
- The distance between 1 and its additive inverse on a number line is: 2
Applications in Algebra
Consider the equation: x + 1 = 0
The solution to this equation is x = -1, which is the additive inverse of 1.
Graphical Representation
On a coordinate plane:
- The point (1, 0) is reflected across the y-axis to (-1, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 1 and Its Additive Inverse
Consider the alternating series: 1 + (-1) + 1 + (-1) + ...
The sum of this series oscillates between 0 and 1, never converging unless 1 is 0.
In Number Theory
For integer values:
- If 1 is even, its additive inverse is also even.
- If 1 is odd, its additive inverse is also odd.
- The sum of the digits of 1 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
Enter a number (whole number, decimal, or fraction) to find its additive inverse: