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repugno
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I'm not sure if this is a sensible question but I'm going to ask it anyway since it's stuck in my head.
Why does Mathematics work?
Why does Mathematics work?
repugno said:Why does Mathematics work?
confutatis said:Math never tells you what you don't already know, so it's not surprising that it never lies.
hypnagogue said:Math never gives you information beyond that contained within the given axioms and the given system of inference. At the same time, it can certainly show you things you don't know (things that aren't yet apparent to you) about the information contained within your axioms + inference system.
given standard logic and the axioms of Euclidean geometry, there is no information in the derived Pythagorean theorem that is not already implicitly contained within the axioms given our rules of logical inference. At the same time, we would be remiss to say that a beginning student who is taught the rules of inference and the axioms of Euclidean geometry already knows the Pythagorean theorem. Deriving the theorem is a sort of unfolding of the collective system to make an implicit consequence of it into an explicit statement, which amounts to a gain in knowledge.
matt grime said:"why does mathematics work?"
what do you mean by work? or mathematics for that matter.
Matt can correct me if I'm wrong, but I have heard that the problem with this proof is just that it takes the equivalent of several books to lay it all out, and no one mathematician however powerful is able to get his mind completely around the whole thing.- selfAdjoint
A geometric sequence is a sequence where each term is multiplied by a common ratio to get the next term. An arithmetic sequence is a sequence where each term is added by a common difference to get the next term.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. It is used to find the length of a missing side in a right triangle.
Probability is the likelihood or chance of an event occurring, expressed as a decimal or fraction. Odds are the ratio of the probability of an event occurring to the probability of it not occurring, expressed as a ratio or fraction.
A quadratic equation is in the form ax^2 + bx + c = 0. To solve it, you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. You can also factor the equation or complete the square to solve for the roots.
The median is the middle number in a set of data when the numbers are arranged in order. The mean is the average of a set of data, calculated by adding all the values and dividing by the number of values.