A simple way to proof that 0,999… is equal 1;
Well… We all hear everywhere that ‘Math is exact!’, but, when I started my Math’s Course I found out that not everything is exactly exact in Math, but, maybe aproximations, by the way good aproximations!
I hope with a easy math writing I can proof to you that 0,999… can be equal 1, but, the question I think probably is hanging out in your mind is: “But, 0,999… is a number, and 1 is another number, 0,999… is too close to 1, but isn’t 1!”, yes, this is true but, let’s think about that, let’s try to make a good and simple demonstration using basic math to proof that 0,999…=1.
Let’s think about 0,999…; we can think that 0,999… can be expressed like a sum of 0,333… how: 0,333…+0,333…+0,333 ( ❤) is equal to 0,999…, we can express like that, right?
So… As we know(or should to know) that 0,333… can be expressed by a fraction 1/3, let’s express ( ❤) by:
So, look that we didn’t change anything, so, if you sum (★) using fractions properties, you’ll have the conclusion that (★) is equal 3/3, and then, this is equal 1! Note that we didn’t changed the results, we just expressed numbers by representatives notations that have the same result and makes sense. So, the final conclusion is:
Then, after you thinked about that, could Math be exactly exact?