The infinity of the infinite line is somehow "bigger" than the Line (or, equivalently, the positive real numbers) is an uncountable infinity. This shows that the infinity represented by the infinite straight Is a reasonably straight-forward argument which shows that any list ofĭefinitely misses out at least one other positive real number. So listing those numbers along the ruler by sizeĬould there be another way of listing them? The answer is no. List you can find a smaller one (you simply insert an extra 0 after But what about 0.001?įor every number you might designate as taking the second place on the Smaller than that, so it should come before 0.1. Clearly the first number should be 0,īut what about the second one? You could try 0.1, but then, 0.01 is One approach would be to order those numbers by size. Can you make a list of those numbers to show that they also form On (the collection of numbers you get from the ruler are called the The number 0, the point half a metre along comes with the number 0.5, and so Point comes with a number: the starting point of the line comes with If you imagine this line as an infinitely long ruler, then each Infinitely many objects: in this case the objects are points on the What about the infinitely long straight line? It is also made up of One, with a place on the list for every object and one object for Objects forms a countable infinity if you can list the objects one by On the list, and then you could count through them, just as you can count You could make a list of all the names, each name taking its own place That's because (with an infinite amount of time) A group of infinitely many people also qualifies as aĬountable infinity. Natural numbers form a countable infinity and that makes sense, as youĬould count through all of them if you had an infinite amount of They distinguish betweenĬountable infinities and uncountable ones. Mathematicians agree with that intuition. Numbers: it is able to fill the gaps between the numbers. To the infinity of the line than to the infinity of the natural This gives a sense that there is somehow more You could place the natural numbers along your line, atĭistance 1 metre apart. Numbers are separate, discrete entities, while the line forms aĬontinuum. Intuitively you might think that the two are different. The same as the infinity represented by the natural numbers? Straight line a line that starts at a point just in front of you and So let's stick to potential infinities those thatĬharacterise something unending. Infinity, and indeed Aristotle thought that actual infinities don'tĮxist in the physical world. This would be something you could measure, You just can't get to the end of thoseĪristotle also thought of another kind of infinity, called anĪctual infinity. Potential infinity: it's definitely there, but you will never actually Infinity is what the ancient Greek mathematician Aristotle called a No matter how long you count for, youĬan never reach the end of all numbers, and you can't reach the end ofĪn unending Universe even if you travel in the fastest spaceship. List, like the list of natural numbers 1, 2, 3, 4. Something that characterises things that never end. If you want, you can join us on the game's Discord, we have a lot of blueprints applying those concepts, and this kind of knowledge is often shared around.In a sense we all have an inkling of what infinity is. Among modules I'd strongly recommend for this combo are super tower 3, neutral amplifier, bulwark and emergency crit. I suggest using serious missile and using a little trick with infinity splash which is that it can "jump" from enemy to enemy, applying the generic and neutral multiplier on each jump, which quickly scales past the amount of hp of basically any enemy as long as you have a strong enough multiplier. Additionally, electricity can deal up to 1000 times it's damage in reflection damage, so if you're barely dying from flat damage, consider disabling it.įor damage don't bother with flat damage at that point of the game. With a script you can get 100% coverage with both of those, and titanium hull is some of the best defense you can have (before forge at least). In order to get a decent amount of infinities, it's preferable to use the temporal barrier/titanium hull combo for defense.
0 kommentar(er)
