Thank you, it took me a while to understand, because I forgot I was talking about prime factors. In fact I was, and the title should be different. My mistake. I'm glad you saw through it. That's a neat explanation by the way. I like math more and more with each passing day.
First of all, pardon me for my poor English, which is even worse for mathematics.
As an answer to my question, I think it does have all the factors n has. But I can't write mathematical proof of it, and so I can't make that statement. It's probably easy. I can write that in the opposite...
Thank you Dave.
I didn't have the need to google that info because the articles people linked were pretty informative and interesting. I just wanted to confirm if I did understand everything from the articles right. Also, there's nothing on the articles about any hazards inside the...
From what I could understand, Jupiter has 2 three-dimensional shapes enveloping it called the radiation belts. They rotate along with the planet. They are formed by high energy particles collected from a constant flow of gases from Io and from the solar winds, and they are collected and highly...
Sorry about my poor English.
I heard Jupiter emits lethal amounts of radioactivity (I don't know what kind). I also read things that suggested that there are areas where this radioactivity is more intense than on other areas.
I wanted to know a few things:
a) why does Jupiter emits so...
The reason why I mentioned the possible need for a proof that does not involves triangles is because this article above uses something called constructible numbers to prove that \sqrt{2} is a number. Using compass and a straightedge, it draws a square with side 1 and then concludes that the...
Yes, one that doesn't assume the existance of triangles or any other geometrical entities other than lines, points and circles. The only one I was taught which I can't quite recall uses the area of four triangles and the area of the square to prove it.
I know this kind of strays from the original subject, but how can I, without the notion of the right triangle and it's properties, and armed only with the notion of perpendicular angles, know that the line that connects two line segments that are perpendicular to each other has the square of...
Because of these numbers being necessary, I thought they were made up, so math could work, even though there would be no exact point whose distance from zero in the real number's line would be the \sqrt{2}, since I had no proof of it's existance. So, when I first asked the post, I thought you...
you are right about the dimensions of length. Sorry, my mistake. About measuring, I was talking more of a hypothetical measuring with arbitrary precision. I thought that was implied. And what I meant was that even if you could measure things with perfect precision, unless you used a unit based...
this was really fun to follow although I wish my compass could change colors like the one from the image because the final result was a mess. The concept of conctructible numbers is much easier to understand and very interesting.
But after following the demonstration, I think I can simplify...
Yes, sorry I don't know what went wrong with the link... I'll try to paste the correct one
Edit: It's fine now. I think I must have copy-pasted it from some post above.
I know, but the proof that can be found here
http://en.wikipedia.org/wiki/Completeness_of_the_real_numbers is beyond my comprehension, so to me if that was the only proof, then it was a matter of faith in the mathematicians because they know what they are doing and they know how to prove it...
You are right! Finally I can put my mind to rest. But what a weird number it is the square root of 2. The fact that I can now envision it geometrically makes it a lot more real and conceivable to me. Thank you!
I'm looking foward to demonstrate this to my teacher who couldn't come up with an...
Reading the article made me realize I've stumbled on something far beyond that which my current scholar knowledge can grasp.
I'll do that. From now on, I'll take a little dose of faith on the mathematicians when I study math. If they say something is true it's because it probably is, and it's...