Tag Archives: Mathematics

Countable and Uncountable Infinity

Hold on to your pants, this might get interesting here. What if I told you that some types of infinity are bigger than other types of infinity? It’s true. Just think about it for a second. The number of positive whole numbers, or natural numbers, is really big, infinite actually, because for the largest number you can think of I can just add one and there’s a bigger number. The set of natural numbers is what’s called “countably infinite” and any set of numbers that can be paired with the set of natural numbers is also considered “countably infinite”. Theoretically, any countable set can have its entire contents listed if the counter were given enough time. However, the set of all real numbers is not countably infinite because for every two values in the set there are infinitely many values between them. In fact, the set of all numbers between 0 and 1 is greater than the set of all natural numbers, that’s what uncountability does.

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Double Post: Subsidies and the Prisoner’s Dilemma

Again, I’m sorry for missing a day, but I’ll do some related topics in today’s double post: Subsidies and the Prisoner’s Dilemma.

Subsidies are support income provided by the government to certain companies, namely agriculture and energy providers. In the past, these sectors were weak and needed support from their companies otherwise life in general would collapse (no food, no electricity, no fuel, etc.). I’m not going to argue that subsidies are not needed, I’m no expert in economics and it’s not my place to do so, but some subsidies, such as those that pay farmers not to farm (which I’ll get to in a bit because it has a little to do with the next topic) are counter-intuitive.

So what does paying farmers not to farm have to do with the Prisoner’s Dilemma? First we have to know what the Prisoner’s Dilemma is. Say we take two prisoners, Alvin and Bruce, who have together committed a crime (the details aren’t exactly important). If either one sells out the other, and the other confesses, the one who confessed gets one year in prison while the one who betrayed gets off free, if both betray each other, both will get three months in prison, and if both confess, both get only one month in prison. It’s, individually, in both Alvin’s and Bruce’s to betray, but it’s in their collective interest if they both confess. We see something similar in raw food prices. If a farmer produce large amounts of food, that food will be worth less due to inflation, than it would be if they produced less, but if farmer produce less food they are at the whim of the markets and could get in trouble due to other farmers potentially producing more food and driving prices down. That’s the farmer’s dilemma, and that’s where subsidies come in.

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Zero

Zero is a number used to signify nothingness, or an absence of quantity. Zero is also often used, in positional notation systems (such as the widely used Arabic numeral system), to allow for large numbers without symbols to represent orders of magnitude. Zero is the additive identity, which means that zero added to any number will yield that number. Although the Babylonians developed a positional notation system, they lacked a placeholder such as zero. The concept of zero arose independently in China, India, Mesoamerica and the Andes. Zero is not prime because it has an unlimited number of factors (anything times zero is zero), but zero is not composite either (zero cannot be expressed as the product of two primes because zero, which is not prime, must always be a factor). The mathematics of zero put forth by Brahmagupta, excluding one rule, are still in use today. The one rule that is not still in use is the statement that 0/0=0. The operation 0/0 is called an indeterminate form and has no clear mathematical value.

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