Create a real world problem which uses the concepts of set, subset, and null set. Write the problem and solve it.
Think of at least three real-life problems that use the idea of infinity and/or negative infinity. They do not need to be strictly mathematical. This can include ideas such as writing poetry, writing a short skit, or drawing a picture. Be creative and have fun!
How big is a million? How big is a billion? How big is a trillion? Think of ways to demonstrate these measures. Name some real-world examples of the use of these numbers.
Make a list of the uses of rational numbers. Think specifically of the subsets we have studied: fractions, percents, decimals, integers, ratios, and proportions. It might be easier to choose one profession in which you are interested and brainstorm to determine how that profession uses these types of numbers.
The concepts of set, subset and null set are widely used in solving real life problems, for example:
I’m on a party and there are 15 dishes available. Some of them are with garlic, I like it, but I don’t want to have a bad breath, though I know that parsley neutralizes its smell. I’ve been informed that there were garlic for 7 dishes and parsley for 8. How many dishes contain both garlic and parsley, so I can enjoy garlic and not have a bad breath?
Solution. G = dishes with garlic, P = dishes with parsley, P U G = all available dishes.
n(G ∩ P) = n(G) + n(P) – n(P U G) = 7 + 8 – 15 = 0.
So it appears that the set dishes containing both garlic and parsley is null. And that I cannot enjoy garlic without having bad breath at this party.
One of the widest applications of the idea of infinity in art is the use of perspective in drawing pictures. In our everyday life calculus is the basis of all technology and computers and it wouldn’t exist without applying the idea of infinity. But in my opinion the most prominent and important discovery ever made using the idea of infinity was the one that has made a beginning to our civilization – the invention of wheel.
One can illustrate such enormous numbers like million, billion and trillion with the following example: if the weight of one hair is one, then million is the weight of 2 standard bags of cement, billion is the weight of 4 cruise ship anchors and trillion is approximately 5 Eiffel towers. Real life examples of use of this numbers are all our units of measure present everywhere, starting milligrams and ending with dollars.
Chemistry has a broad use of all the rational numbers: fractions, ratios and proportions are used when calculating necessary quantities of substances for reactions. Percents and decimals are used in computations of mass, volume and content. Integers are used to represent the numbers of elements in periodic table or quantities of protons and electrons present in atoms.