I ended up having my mind blown today that 0.999... equals 1. I thought so hard about this and it practically killed me. Proof? 0.999... = 0.9 + 0.09 + 0.009... 0.999... = 9/10 + 9/100 + 9/1000... t1= 9/10 r= (9/100) ÷ (9/10) = (1/10) S∞= t1 ÷ (1 - r) S∞=(9/10) ÷ (1 - 1/10) S∞=(9/10) ÷ (9/10) S∞=1 Sorry I just found this crazy and my inner math nerdiness had to share. HOW DOES IT MAKE SENSE
The number 0.9999... could go on forever, technically it's an infinitely tiny gap between 0.999... and 1. At some point, the number needs to reach 1, but it wont, because the period of 0.999 will go on forever. At some point, 0.9999... equals with 1 since the gap is so tiny that we can't see the difference. However, the math you did there would be easier to understand if hand-written. This is a mathematical problem. Can't solve it. You gonna get a Nobel-award if you solve this issue.
it sort of is already solved but at the same time not. The only way it's possible to be real, is if we can actually accept into our maths that there can be infinite decimals such as this. And no it's not that the difference between the two would be so small you'd round it up. It literally equals 1. I'm told the reason why we find it so strange is due to the fact that we don't really accept infinite decimals into our current math systems. We can't actually use words to describe why this is because they don't exist. It's like a while back when negative numbers were first discovered into our math system. How can someone have -5 cookies and loose -3 of them? It doesn't really make sense but we somehow accept it in today's math. I can name the variables if that helps? t1 is term 1 (9/10) r is the ratio between each term. S is the sum of all of the terms. Hope this helps xd
