123rock

The very definition of cosine is in terms of radians and thus the cosine of 1 radian or cos(1) would be cos(1/pi) since there are 2pi radians in a circle.

Something has to be proven to be undefined before you can say it is. Besides, it's not a relatively hard question to imagine, of how many times 0 fits into 0, or how many monkeys can put zero bananas into zero baskets. I guess in that case it's undefined, but tautology is not mathematics, and before you can state that something is undefined solely based on a mathematical dictionary definition, you have to show it. Edit: Also, if you state that 0/0=0 and no other number, it leads to absolutely no contradictions whatsoever

That's the disproof that 0/0=1. If 0/0 doesn't equal 1, then 0/0(x) does not equal x, which is true for all numbers except for x=0. I never said that was a proof. Why not take me seriously Dave? The simple arithmetic is right there.

By the laws that you have set forward, your own statements contradict you: If 1=1, in which is the only case that these monads can be stable, then 1-1=0, and thus 1_0+0_1=1_0_1=0 What is 1_0_1? Nobody knows from what you've explained. Please elaborate on how this can describe nature? Also, if 1_0=1_0, then 1_0+0_1=0_1+1_0, and thus 0_1_1_0=0_1_0=1_0_1

So 1_0_1=0=0_0?!??!?!?

I never said that you have to evaluate 1/0, or x/0. While still a fraction, x/0 applies to the same laws of arithmetic as all other fractions. 0/0=x and x * 0=0 are not the same equations because multiplying each side by zero in 0/0 (0)=x *0 implies that 0/0 is 1. If 0/0=0/0, which would be the only way that it can be undefined, otherwise 0/0 can equal whatever we want it to equal, then 1-1/0=0/0

The only way that this equation works for is if n and C are both constants of 1, and X sub Y increases by one for y+1, when y starts out at 0

well I know that x/0 is undefined, and I'm not saying that 2=1 because that would be a contradiction to the whole proof that 2=1. I guess it would be logical to express 1/0 as how many times 0 goes into 1, but that obviously doesn't work for 0, since it would be R and i, so it's better to use a pure mathematical proof rather than kindergarden taught logic of how to skip steps to get the same results because they obviously don't work for x/0. If the same arithmetic principles for x/0 didn't apply as they do for all numbers, i.e. x/0-x/0=0/0 then the proof that 0/0 isn't R, and i is useless, as 0/0=1. Since you can't multiply 0/0 by anything, or substitute it with anything, 0/0 will have different values yet since you couldn't substitute 0/0 by anything, by definition 0/0 wouldn't be 0/0 and thus the problem. What I mean is that 1/0-1/0=0/0 is a perfectly legal operation.

Hmm, I pondered over this question too, but it is not the galaxies that are moving away, it is the space that is expanding in the 4th dimension, and since space isn't really a "thing" it can travel faster than c with no problems. It is only explained that the galaxies are moving away from us, because those are the observable effects, but they aren't really the object that's moving away, just a method to explain what is observed kind of like teaching that the reciprocal of a fraction is when you flip its denominator with its numerator, instead of doing the algebra to prove it.

ok 1/0=2/0 because 1/0(2/2)=1/0 2/0=1/0 We are not evaluating x/0. We are just operating on the numerator and denominator which are still defined values.

Although this loop is a paradox, it can also be stated in this manner where you do have free will. For example, if you time travel in the past and save your mother as a child from dying, you will most certainly be alive to do it and thus no paradox. Or if you want an example for the future, then you go one year in the future and see a theorem with its proof published somewhere. You go back in time, teach it to a student, and he publishes it the following year. Such examples however do not make sense, because who taught the theorem to the student? The time traveler. And where did the time traveler see the theorem? From the student, thus the theorem virtually came out of nowhere. In your example, you are assuming that you go back in time. With that proposition, you might as well not have free will, but fastforwarding in time doesn't have any limitations.

ok, the ratio of 1 to 0 isn't a function since it would have to equal to 0/0 as well as x/0, thus 1/0 isn't R, or i, may or may not be 0, infinity or undefined.

Ok, so if 10/5 is 2, what does the 2 signify? It's a process of evaluation. if 0/0=0/0 by definition, then 1-1/0=0/0 by arithmetic. What proof can you show me that 1-1 doesn't equal 0? Mathematicians have said 0/0 is undefined because they have found that it's undefined through standard mathematical processes not the other way around, saying that you can't use standard mathematical processes to show what 0/0 is because it's undefined and thus is undefined. This is faulty logic Aeschylus. P.S.: Tell your dog good job.

Two men meet in a clinic. The first one has a red ring around his penis, the second one has a green one. They're both worried. The first one goes in, comes out and tells the other,"Oh, don't worry, it's nothing." Calmed down, the second one comes in. The doctor tells him,"Hmm,this looks serious." The man immediately got worried and asked the doctor,"What do you mean, that man that just came out said not to worry!?" The doctor said,"Well lipstick is much more different than gonorhea."

if 1-1=0, then 1/0-1/0=1-1/0. You can simply think of this as 1-1=0, then dividing by 0 when everything is defined. When the denominators are the same, the numerators can be subtracted added, etc, thus there is no reason to think that the same ratio can't be subjected to arithmetic. The only way 0/0 is undefined is if you try to evaluate it. 0/0(2) is not undefined, but 0/0. Theological proof like it is undefined so you can't prove it's defined is the most inconsistent, and the way many theorems have been proven is by proving the inverse of the false assumption. One such case is sqrt.of 2=a/b. Since sqrt. of 2 is irrational, a/b cannot describe it, but it is assumed that it can be described by a/b, thus proven not true. Same here, we assume that 0/0=1, and prove that it can't, and thus arrive that 0/0 may or may not equal 0, infinity, or just undefined. Mathematics is not about going with the flow and accepting proofs, but finding them, and thus show me why 0/0 is undefined and not simply 0? Since 0/0=1/0, then i guess 1/0=0, if 0/0=0, but then does that make sense?

What?

Anyway, haven't you guys heard of the Brazilian ants that gather at numbers that make them have an area of 2miles wide and 10 miles long. Some people should really read Leiningen vs. the ants. If the ants had an IQ high enough to decide to wipe us out, then believe me they can do it. But that is IF they have an IQ, or maybe they do