4 Additive Inverse :
The additive inverse of 4 is -4.
This means that when we add 4 and -4, the result is zero:
4 + (-4) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 4
- Additive inverse: -4
To verify: 4 + (-4) = 0
Extended Mathematical Exploration of 4
Let's explore various mathematical operations and concepts related to 4 and its additive inverse -4.
Basic Operations and Properties
- Square of 4: 16
- Cube of 4: 64
- Square root of |4|: 2
- Reciprocal of 4: 0.25
- Double of 4: 8
- Half of 4: 2
- Absolute value of 4: 4
Trigonometric Functions
- Sine of 4: -0.75680249530793
- Cosine of 4: -0.65364362086361
- Tangent of 4: 1.1578212823496
Exponential and Logarithmic Functions
- e^4: 54.598150033144
- Natural log of 4: 1.3862943611199
Floor and Ceiling Functions
- Floor of 4: 4
- Ceiling of 4: 4
Interesting Properties and Relationships
- The sum of 4 and its additive inverse (-4) is always 0.
- The product of 4 and its additive inverse is: -16
- The average of 4 and its additive inverse is always 0.
- The distance between 4 and its additive inverse on a number line is: 8
Applications in Algebra
Consider the equation: x + 4 = 0
The solution to this equation is x = -4, which is the additive inverse of 4.
Graphical Representation
On a coordinate plane:
- The point (4, 0) is reflected across the y-axis to (-4, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 4 and Its Additive Inverse
Consider the alternating series: 4 + (-4) + 4 + (-4) + ...
The sum of this series oscillates between 0 and 4, never converging unless 4 is 0.
In Number Theory
For integer values:
- If 4 is even, its additive inverse is also even.
- If 4 is odd, its additive inverse is also odd.
- The sum of the digits of 4 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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