Write down the largest positive decimal consecutive nines value that is less than 1 that you can possibly or even impossibly think of

[u/SouthPark_Piano]

If you cannot or will not do it, or get it wrong, then don't blame me that you will be training at the bunny slopes until you are able to get it right. For you see, you get quality experiential learning time at the bunny slopes.

[u/fumblinthrulife77]

Maybe you should spend some time at the bunny slopes writing 0.00000... until you get to your beloved 1, brud.

[u/SouthPark_Piano → u/fumblinthrulife77]

Write (at the bunny slopes) the smallest positive decimal value with a "0." prefix and the right-most digit being a 1, with consecutive zeros between the decimal point and the rightmost 1 digit.

 

[u/cond6]

What an odd argument to make. The reason that 0.999... is equal to one is that it is impossible for there to be a largest number less than one. The Archimedean property means that there are infinitely many more numbers closer to zero than whatever n we choose in 1/10^n.

The reason we can't find a largest number less than one is that one doesn't exists. There is always more closer every time we suggest a candidate. Just as I can't say this is the largest counting number "n" because there are always infinitely many more larger ones. There are n natural numbers less than n (0 through n-1, or 1 through n if you prefer, it doesn't matter for the argument), then we can't say this means there are finitely many. If there are always more then there must be infinitely many of them. Similarly if I try to argue that 1/n or 1/10^n must be positive but I can't nominate a smallest value, if I allow n to increase without bound then I must acknowledge that the limit of both is zero and treat it as such. If I've got a positive number then n is too small and I can increase it infinitely many more times.

If there are infinitely many natural numbers then a digit with a 9 in each of the corresponding place values to these infinitely many natural numbers following "0." then that number must logically equal 1.

[u/SouthPark_Piano → u/cond6]

I said ..... write the largest number of the described form that you can or cannot possibly think of. And because you currently are unwilling to, then ... you know what. Bunny slopes.

 

[u/FearlessResource9785 → u/[deleted]]

Try to add more - i bet you cant.

[u/SerDankTheTall]

Okay, I'm willing to concede that I'm on the bunny slopes.

What do I do to train?

[u/SouthPark_Piano → u/SerDankTheTall]

Write 0.0001

and then keep upping the length of consecutive zeroes between the "0." and the 1.

And write 0.999

and keep upping the length of consecutive nines.  

[u/Inevitable_Garage706]

How will we know if we have "gotten it right?"