The Laws of Mathematics are Unchangeable

Thank you for your little math lesson. "How do we know such a set of laws exist? Where is the evidence for this?" Okay, mathematics, like physics, is a branch of science. The laws of physics have existed since the dawn of time, and the laws of physics aren't written down anywhere. We are slowly discovering all of these laws of physics. We humans don't have the power to change the laws of physics. These things that apply to physics apply to mathematics as well. At the dawn of time, if you wrote the equation xï¿½-x-6=0, then used the quadratic formula, which is: x=(-bï¿½√(bï¿½-4ac)/2a, then you would get the two solutions to the equation, x=3 and x=-2. http://en.wikipedia.org... However, the quadratic formula was first discovered in 628 BC http://en.wikipedia.org.... I say discovered instead of invented because it still existed, but we just didn't know that it worked, refuting your point. It existed long before we thought of it and wrote it down. We didn't invent math; we just discovered that it worked and applied it. The same applies for physics, when long before Newton was born, if you pushed an object into frictionless space, it would continue to move without acceleration until an unbalanced force acted upon it. "Guesses far from describe what we currently know about infinity. The examples I cited have been rigorously proven by various mathematicians." Anything that a mathematician can prove without a doubt is a law of mathematics. If a proof is disproven, then it obviously wasn't proven without a doubt. Now, about what Aristotle said, "Since no sensible magnitude is infinite, it is impossible to exceed every assigned magnitude; for if it were possible there would be something bigger than the heavens." Aristotle was attempting to apply mathematics, by comparing the infinite to the heavens. Applied math, such as physics, is different from regular math, as you already said, "With the note that applied math is mathematics - physics for example is applied math." Just because we make different guesses about infinity, doesn't mean that infinity constantly changes. The concept is just sitting out there, laughing at our mistakes, waiting for us to finally discover and prove what it really is. (Note: That sentence there was metaphorical, not literal.) "What I am saying here is that you cannot restrict mathematical systems by saying that you cannot change aspects of it." My argument against that is that changing the base number of the system doesn't change the actual values of the number. In our ten-based system, 7 is supposed to represent seven, but in the binary system, 111 is used to represent seven. The laws of mathematics do not use symbols to represent values; they use values. The symbols were come up with by humans. The values were not. (Note: In my explanations, numerals are symbols, while words are values.) It is common knowledge that two times two is four. We commonly express this as 2x2=4. If you were to use a binary system, this would be expressed as 10x10=100 (which, ironically, is a real solution in either system). In both cases, two times two is four. We may read it in a different way depending on the system we're using, but in "natural" laws of math, the values are all that matter. "Changing bases are an integral part of math, and discarding them from this argument is similar to discarding addition and the likes." This is beyond the unchangeable laws of math, as this is just our interpretation. "Again, I apologize if I was not clear here." Don't worry, you were loud and clear; I just disagreed with you. "What I am saying is that we, as humans, have laid down the basic laws of math. The most basic principles are ones that we have set down which cannot be proved...." No, we have not. We have discovered them. Math is both very abstract and very real. We did not decide that two plus two is four; we discovered it when we put two apples with two oranges. We did not decide that five times three is fifteen; we discovered it when we laid out five rows of three pebbles, and counted them. "Because math is a creation of man, and therefore its laws can change, also because changes in base change mathematical laws, the laws of mathematics are changeable and the resolution is negated." CONCLUSION: Because math has always existed, its laws are "set in stone", and we as people can only discover new aspects of math. Change in base does not change the values of the numerals, thus not changing the law that is applied to it. The laws of mathematics are unchangeable, and the resolution is confirmed. Thank you, and I look forward to a brilliant response.