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.