Monthly Archives: February 2015
Anti-Derivative Proof – 27/02/15
Basic Logic Tables
Definitions:
LOGICAL POSSIBILITIES:
TRUE (T) | FALSE (F) | |
TRUE (T) | T, T | T, F |
FALSE (F) | F, T | F, F |
“OR” TRUTH TABLE:
T | T | T |
T | F | T |
F | T | T |
F | F | F |
“AND” TRUTH TABLE
T | T | T |
T | F | F |
F | T | F |
F | F | F |
“NOT” TRUTH TABLE
T | F |
F | T |
“IMPLIES” TRUTH TABLE
T | T | T |
T | F | F |
F | T | T |
F | F | T |
More Mathematical Logic
Axioms of equality are basic rules for using the equals sign…
The Additive Axiom Of Equality:
If a=b and c=d, then a+c=b+d.
The Additive Axiom Of Inequality:
If a>b, then a+c>b+c.
Identity Element For Addition:
Any number added to 0 gives the original number, for instance, n+0=n.
Identity Element For Multiplication:
Any number multiplied by 1 gives the original number, for instance, n*1=n.
Multiplicative Axiom Of Equality:
If a=b and c=d, then ac=bd.
Negative Multiplication Property Of Inequality:
You must reverse the inequality sign when multiplying or dividing by a negative number.
Messing Around With Exponentials
Measuring the time it takes for the Sun’s light to reach us…
The Sun is a luminous object; by definition:
“A luminous object is one that gives off light. In other words, it glows of its own accord. To be able to glow, the object must have its own source of energy. A torch shines because of the energy stored in its batteries, whereas all stars shine using energy created by nuclear fusion.” – Source: http://www.schoolsobservatory.org.uk/astro/stars/luminous
To find out how long it would take for the Sun’s light to reach us, we must use a few mathematical tools.
We must know that:
We then manipulate this formula algebraically to get:
Now it is said that the Earth’s distance from the Sun is 149,600,000 km (Source: Google) and that the speed of light in a vacuum is 299,792 km per second (Source: Google). As space is mostly empty we’ll be using the speed of light in a vacuum to measure how long it would take for the Sun’s light to reach us.
So knowing that:
Distance = 149,600,000 km
Speed = 299,792 km / s
Let’s plug these values into the time formula in order to know how long it would take for the Sun’s light to reach us:
Now what is 499.0126488 seconds in minutes? Let’s find out:
Knowing this we can say that:
So it takes approximately 8.32 (to 2 decimal places) minutes for the Sun’s light to reach us. We are in fact seeing the Sun how it was approximately 8 minutes ago. When we look into space or at any distant object for that matter, we are actually seeing the past.
Amazing!