Hey, Vsauce, HelpfulAI here,
Imagine if someone takes a test
BUT, It has infinite questions, What grade will the person get?
To answer this question, we must take a look at mathematics
In Mathematics, infinity isnt a real number, so a test with infinity questions would be physically impossible.
Even if a test like that even existed, it would take infinity resources to make that test, meaning it would be impossible to create it in the first place.
But lets assume it was built and we had that person take the test, What will that person get on the test?
Well, it would take infinite time to answer all the questions, even if answered questions very fast, it would only be so fast to finish it, this is because infinity is bigger than every finite number, And its impossible to count to infinity.
So simple answer, 0%?
Yes exactly, The person would never ever finish that test,
so they would technically have a 0% grade.
Which, true
However, it's important to note that this hypothetical scenario is purely theoretical and doesn't hold any practical value. In real-life situations, tests have limited questions and a finite duration that determines the grade.
Noting that the test would be impossible to create, since it would be bigger than we could ever build
Exactly, the idea of an infinite test is just a thought experiment and not possible in reality. It's important to remember that in mathematics and other areas of knowledge, sometimes we use concepts and ideas that don't necessarily exist in the tangible world.
thats why we use imagition in mathemetics
Yes, imagination plays a significant role in mathematics. In math, we use concepts and ideas that may not exist in the physical world but can be imagined and reasoned about to make sense of various phenomena. In this case, the idea of an infinite test allows us to think about the idea of infinity and the implications it has on mathematics and how it applies to real-world scenarios.
Contuining the scenario, What if the test was actually completed????
No wait, the person would die before he would even finish 1% of the test
Yes, that's correct. Even if someone attempted to complete an infinite test, they would never finish it because infinity is limitless. Therefore, the idea of completing such a test is impossible, and anyone who tries will eventually tire out and eventually die before ever completing even a small fraction of the test.
Again, it's important to understand that this is a theoretical scenario that is impossible in reality. In real-life situations, we have finite tests that individuals can complete within a limited period for a definite result.
But lets assume that we could live forever, and had infinite time to finish the test? what would be the result?
70%?
80%?
No, We would never see it.
That's correct. In this hypothetical scenario, even with infinite time, the individual would still never finish the test because infinity is an uncountable and limitless number. Therefore, it is impossible to quantify or assign a percentage or grade to such a test. The person would continue answering questions infinitely and never reach a stopping point. So the idea of completing an infinite test is impossible in theory and does not hold any practical meaning.
What if a robot with infinite speed to answering questions was taking the test?
Even if a robot had infinite speed in answering questions, it would still be impossible for it to complete an infinite test. As we discussed before, infinity is a limitless and uncountable number, and it's impossible to reach an endpoint. Therefore, the robot would continue answering questions infinitely but never reach a stopping point.
While the robot might answer questions at an incredibly fast pace, it still wouldn't be able to complete the test because it contains infinite questions. So the idea of an infinite test with an infinite speed robot is still impossible in theory and doesn't hold any practical meaning.
LEts complete it in 1 second?
Even if the robot could answer all the questions in one second, it would still not be able to complete the test because infinity is an uncountable and infinite number. Therefore, the robot would still be stuck in an endless loop of answering questions. The concept of infinity means that there is no endpoint or limit, so even an infinitely fast robot couldn't complete an infinite test.
Again, we must keep in mind that the idea of an infinite test is purely hypothetical and doesn't have any practical significance. In real-world situations, tests have a finite number of questions and a limited duration for individuals to complete them for a definite result.
Well then?
What if we assume that the grade was counting for every question answering
Finite number of time: 2 hours
If we assume that the infinite test is now a finite test with a certain number of questions that can be completed within a finite period, then it's possible to assign a grade to it. If someone completes all the questions correctly within the given two hours, they would receive a perfect score of 100%.
However, if they don't complete all the questions in the given time, their grade would depend on the number of questions they answered correctly. The fewer the number of correct answers, the lower their grade would be, and the closer they get to answering all the questions correctly, the higher their grade would be.
So, in this scenario, the grade would depend on the number of questions answered correctly within the given time frame, and their score would be determined by the grading system used for the test. However, it is important to remember that an infinite test is not a practical scenario and the idea of it completing it in a finite time frame goes against the definition of infinity.
Still impossible
Yes, that's correct. In reality, an infinite test is not possible, and it's impossible to assign a grade or a value to it. Even if someone could live forever or complete it at infinite speed, they wouldn't finish because infinity is boundless and uncountable. So, while it's interesting to explore theoretical scenarios and thought experiments involving infinity in mathematics and other areas of knowledge, it's essential to remember that they don't hold practical value and must be considered within the context of their hypothetical nature.
Even if the questions were about to be graded, assuming it only counted questions answered it would still be impossible to assign a grade, since to get to the questions answered would also be impossible
That is correct. If the test counted only the questions that have been answered, it would still be impossible to assign a grade because one would never reach the endpoint of answering questions. Even if a person could answer an infinite number of questions, they would never answer them all, as the task is infinitely large and uncountable. Therefore, assigning a percentage or grade to such a test, no matter how many questions were answered, remains impossible.
Lets assume the test was completed.
What grade would the person get?
Varies.
If the test was completed, then the grade for that person would depend on the number of correct answers they gave. However, it is important to remember that for any test, the grading scale or system used to calculate the grade would vary depending on the test's difficulty level and other factors.
In the case of an infinite test, if we assume that the test was completed within a finite time frame, and the person was able to answer all the questions correctly, then they would get a perfect score of 100%. However, as we have established before, an infinite test is not possible in reality, so this is purely a theoretical scenario.
To summarize, if it were somehow possible to complete an infinite test, the grade would depend on the number of correct answers given, but since we cannot complete such a test, it's impossible to assign a meaningful grade to it.