I am nearing the end of my physics degree at a top university and I have not seen an error free proof that that 0.9999 recurring and 1.0 are one and the same.
I am nearing the end of my physics degree at a top university and I have not seen an error free proof that that 0.9999 recurring and 1.0 are one and the same.
f = 0.99 Multiply both sides by 10, 10f = 9.99 Both numbers are recurring and so there is a nine in the same position after the decimal point in both equations. Subtracting the first from the second gives: 9f = 9 Divide both sides by 9 and you have f = 1 Now, this is a rather simple idea; one that I'm guessing you already understand. You did post this in the philosophy section, and so I'm assuming that your thread is not meant to be taken literally. Could you clarify this please?
f = 0.99 Multiply both sides by 10, 10f = 9.99 Both numbers are recurring and so there is a nine in the same position after the decimal point in both equations. Subtracting the first from the second gives: 9f = 9 Divide both sides by 9 and you have f = 1 Now, this is a rather simple idea; one that I'm guessing you already understand. You did post this in the philosophy section, and so I'm assuming that your thread is not meant to be taken literally. Could you clarify this please?
If we perform operations such as multiplication, addition, subtraction on numbers that go on forever, you would need to prove your answer by breaking your method and applying these operations on the seperate numbers. This would take an infinite amount of time and cannot be completed.
All solutions that I have seen only demonstrate a 'limit towards 1 answer'. They do not demonstrate that 0.9999 recurring is exactly 1.
If we perform operations such as multiplication, addition, subtraction on numbers that go on forever, you would need to prove your answer by breaking your method and applying these operations on the seperate numbers. This would take an infinite amount of time and cannot be completed.
All solutions that I have seen only demonstrate a 'limit towards 1 answer'. They do not demonstrate that 0.9999 recurring is exactly 1.
Yes, but providing that infinity - infinity = 0, this method should work.
Why don't you prove to us that 0.999 recurring does not equal 1?
The tools I would employ would be as erranous as the tools used to prove that they are equal.
Consider comparing the first digits of both numbers. 1 is greater than 0. I seek to find the difference by comparing the next digit. But the '9' is greater than the zero in 1.0. So I seek to find the difference in the next digit etc....
All the methods employed are based on 'limits' and not equivalence.
I am nearing the end of my physics degree at a top university and I have not seen an error free proof that that 0.9999 recurring and 1.0 are one and the same.
What "errors" do you mistakenly think you have discovered?
I can't believe I'm even answering this but they are the same number.
Actually...I'll concede that I'm not qualified to comment on this topic because my knowledge of maths doesn't go beyond A2 Level, and it's not something I've ever encountered.
I can show two numbers are different by stating a number that lies between them.
3 is not the same as 7 as 6.254 lies between them.
Try stating a number that lies between 0.9˙ and 1.
I'm not deliberately trying to be a dick but you would have to prove that necessarily two numbers are different if and only if there is a number between them.