... biggest number. You can prove this with a simple proof by contradiction. Proof: Assume there is a largest number, n. Consider n+1. n+1*n. Therefore the statement is false and its contradiction, "there is no largest integer," is true. This theorem is valid based on the "Validity of Proof by Contradiction." In 1895, a German mathematician by the name of Georg Cantor introduced a way to describe infinity using ... ...}. This concept seems a little off at first, but if you think about it, it makes sense. You can add 1 to any integer to obtain the next one, and you can also add 2 to any even...

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• Approx Pages: 4
• Grade Level: High School

... teaching this objective are the divisibility test for 4 and the divisibility test for 2. The divisibility test for 4 states an integer is divisible by 4 if, and only if, the last two digits of the integer represent a number divisible by 4. The divisibility test for 2 states an integer is divisible is divisible by 2 if, and only if, its unit's digit is divisible by 2. These tests make ... ...

• Word Count: 734
• Approx Pages: 3
• Grade Level: High School

... . He claims the proof is "remarkably simple". Let p be a prime and q=1 x 2 x 3 x x p+1; That is, one more than the product of all the integers from 1 through p. The integer q is larger than p and is not divisible by any integer from 2 through p, inclusive. Any one of its positive divisors, other than 1, and any one of its prime divisors, therefore, must be larger than p. It follows that ... ...

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• Grade Level: High School

... , would produce the number -1" (Bunch, 2000, p. 303). The squares of positive and negative numbers always come out positive; therefore there was seemingly no solution to quadratics that resulted in a negative integer. As Engel continues on to state, "Solutions for equations like these can be found, however, if we decide to invent a completely new number whose square is -1; of course, it is ... ...

• Word Count: 1237
• Approx Pages: 5
• Has Bibliography
• Grade Level: High School

... from conventional geometry, which deals with regular shapes and whole-number dimensions. Examples of this are lines and cones. Fractal geometry deals with shapes found in nature that have non-integer, or fractal, dimensions, or lines, like rivers and cone-like mountains. Fractal geometry developed from Benoit Mandelbrot's study of complexity and chaos. He published a series of fluctuations of the stock ... ...

• Word Count: 551
• Approx Pages: 2
• Grade Level: High School