This is inspired by the YouTube video:
After you watch this video, these “seven deadly sins” of mathematics are relating to both zero and infinity. And these seem to look as they might not be solved, but please just look at the other angle. I have already debunked these “seven deadly sins” to become solvable problems. To solve these problems, there are many perspectives of mathematics, whether is pure mathematics or discrete mathematics, it all comes to just simple logic. Assume that zero and infinity are numbers or just variables with value in terms of algebra. I have a little background on computer science, so I might think of zero and infinity as binary values with one replace by infinity.
0 / 0
This problem can be debatable. For applied mathematics and sciences, if zero is divided by zero, it equals to zero because both numerator and denominator carries no value in its quotient realistically. But, in the pure mathematics' perspective Any number where its factor multiplies by itself by a power divided by the same factor or the number whose factor multiplies by itself by another power will have the power reduced by the power of the factor of the divider. So by dividing zero by zero, the power of zero is reduced to zero. According to power laws, any number with an exponent of zero is one, so zero to the power of zero is equal to one.
∞ / ∞
Same application for 0 / 0 in a pure mathematics perspective. Dividing infinity by infinity reduces its power from one to zero, and therefore, infinity to the power of zero cancels out to equal to one.
0 x ∞
By using the AND logic gate, assume that infinity has a value and zero has no value. Note that any number multiples with zero end up with zero because zero cancels out any value. Therefore, when zero multiplies by infinity, zero cancels out infinity, therefor the product is zero.
∞ - ∞
Assume infinity has a value. Infinity has an infinite value which is left undetermined because that number is huge. But when is subtracted by the infinity which is the same value which is left undetermined and infinity can be negative as it is an integer, this problem can be rewritten as : ∞ + (- ∞) , and if a number is subtracted by the same number, the difference is zero. As a result, ∞ - ∞ = ∞ + (- ∞) = 0
There are two methods to solve one to the power of infinity, but ending with the same answer. The pure mathematics method states that one to the power of any number still equals to one while zero to the power of any number still equals to zero. This applies to calculations in physical sciences. The discrete mathematics and digital logic method is an infinite value of AND gates whose inputs are both similar in terms of value: if both inputs of the AND gate are 0, the output from the AND gate is 0 and if both inputs of the AND gate are 1, the output from the AND gate is 1. My reasoning is that zero and one are binary numbers which do not change in value when they multiply by themselves to the power of any number. As for -1 to the power of infinity, there are two solutions which are +1 (assume infinity is an even number and any negative integer that is squared is equal to a positive integer) and -1 (assume infinity is an odd number). Infinity can be both positive and negative. Therefore, any value except -1, 0, and 1 to the power of infinity will have a number that will not exists, whether the integer is positive or negative.
Note that sixth and seventh deadly sins is referred to first and second deadly sins which is explained and solved.
Hing Wen Yi (hingwenyi12345@gmail.com) is a content creator under the Newswav Creator programme, where you get to express yourself, be a citizen journalist, and at the same time monetize your content & reach millions of users on Newswav. Log in to creator.newswav.com and become a Newswav Creator now!
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