heres a cool proof, see if u can prove why its wrong
x=y Multiply both sides by Y
xy=y^2 subtract both sides by x squared
xy-x^2=y^2-x^2 factor both sides
x(y-x)=(y+x)(y-x) divide out a y-x from both sides
x=y+x since y=x, y+x=x+x, and x+x = 2x
x=2x divide out the x
1=2
You're dividing by zero (y - x), and your proof is invalid.
Writing 999's to the last infinite place does not equal a power of 10, only a power of (10)-1.
Same with writing an infinite number of 9's when a decimal point is placed Infront of it
It never becomes 1, it never ever reaches 0 or even 1-(1/infinity).
It reaching 1/infinity as a concept but the lines never meet.
There isn't an argument that needs to be made. Under the rules of real numbers and infinite decimal representation, .99999999... and 1 are the same number because there is no real number in between them, and 2 different real numbers must have another real number in between them.
If your argument involves anything like limits or algebraic manipulation, it's just wrong. Just use hyper real numbers and it no longer works. Any actual proof must invoke properties of the real numbers.
Wrong you cannot count the irrationals in any order you put them. There are infinitesimal length between all reals.
Writing 999's to the last infinite place does not equal a power of 10, only a power of (10)-1.
Same with writing an infinite number of 9's when a decimal point is placed Infront of it
It never becomes 1, it never ever reaches 0 or even 1-(1/infinity).
It reaching 1/infinity as a concept but the lines never meet.
You're still stuck on the basic concept. Writing ".999..." is already 1, there's no "it never reaches/becomes 1". That's an artifact of our imperfect representation of numbers. Three thirds *is* one, and ".333..." *is* one third.
Pi also has a value. You can't say "there's no Pi, because writing the number out never finishes resolving". It just can't be expressed/communicated to someone using base ten math, in English or any other human language. You aren't capable of understanding or expressing infinity except indirectly.
I notice you've come back, but "accidently" skipped the posts and the videos that refute your position quite handily. Which include the "there is no number small enough to fit between .999... and 1" proof. But let's face it, the real reason that people fall for this is that they have this mistaken notion that writing "..." implies that the value in question is not resolved and that writing .999... is shorthand for physically writing an infinite number of 9s. It isn't. Nobody questions the number 1, or the number 1 expressed as 2/2, 3/3, 4/4, etc. But suddenly when it's written in decimal form (base 10), you balk, because you can't figure out that this is a limitation of expression in base 10 involving dividing by thirds, not of the numbers themselves, which never change. Stop thinking in base 10, which was an obvious but ill-fated choice for humanity to make. Math expressions are a lot easier using bases that are powers of two.
In Base 9, what do 3/9, 6/9, and 9/9 evaluate to?
Writing 999's to the last infinite place does not equal a power of 10, only a power of (10)-1.
Same with writing an infinite number of 9's when a decimal point is placed Infront of it
It never becomes 1, it never ever reaches 0 or even 1-(1/infinity).
It reaching 1/infinity as a concept but the lines never meet.
You're still stuck on the basic concept. Writing ".999..." is already 1, there's no "it never reaches/becomes 1". That's an artifact of our imperfect representation of numbers. Three thirds *is* one, and ".333..." *is* one third.
Pi also has a value. You can't say "there's no Pi, because writing the number out never finishes resolving". It just can't be expressed/communicated to someone using base ten math, in English or any other human language. You aren't capable of understanding or expressing infinity except indirectly.
I notice you've come back, but "accidently" skipped the posts and the videos that refute your position quite handily. Which include the "there is no number small enough to fit between .999... and 1" proof.
All Reals can be deducted as the limit of rational numbers. As is true of pi.
1/3 is the infinite limit of negative powers of 10, multiplied by 3. However the limit itself is never reached.
(2^1)+(2^0)+(2^-1)+...+(2^-infinity) never reaches (2^-infinity) actually. ANYMORE than (2^1)+(2^2)+(2^3)...reaches 2^infinity. It is infinitely small for the 1st series and infinitely large for the 2nd. It cannot terminate to a measurable real number.
What is the difference between 0.999 infinitely and 1 itself. Not 0 as is required for them to be the same number. But 1-(10^infinity) which is only a concept but not a countable quantity.
0.999 ad infinitum goes to infinity but does not actually reach it.
Stop thinking in base 10, and you won't have this perception problem. What do one third, two thirds, and three thirds evaluate to outside of base 10?
Does (2^0)+(2^-1)+...(2^-infinity) Ever reach the number 2, at (2^-infinity)?? Nope it just goes on INFINITELY and never becomes it.
Same with your endless 0.333's and 0.999's.
Nope it's not, Sir.
Remove the decimal all together and it does not become a "round" number - EVER. See?
As many 9's as you add it never becomes an exponent of 10, or (10^0)=1 INCLUDED. Always (10^infinity)-1
YOU CANNOT ARGUE WITH THIS. Or fault the reasoning behind it
you high school drop outs should go read page 27 and maybe a few things before that.
I thought that link looked a little suspicious. I got this when clicking it.
As many 9's as you add it never becomes an exponent of 10, or (10^0)=1 INCLUDED. Always (10^infinity)-1
YOU CANNOT ARGUE WITH THIS. Or fault the reasoning behind it
You keep asserting this, while ignoring the arguments that refute you. If you can address the post with the 2 videos in it, arguments and videos, *then* you could try to claim "YOU CANNOT ARGUE WITH THIS"...it still wouldn't work, but at least you would have a leg to stand on.
Nope! I won.
Math is not a democracy. It doesn't matter how many idiots vote in something it still does not make it legit.
Absolutely correct. To add on to what you’ve said, 3/3 is equivalent to one therefore .999 repeating is equivalent to one.
I actually asked a friend of mi e this question this week to see what he‘d say. Pretty good at math. Said no, blah blah. Proved it to him and he was amazed. Would you say in practice it is not equal but in theory it is?
Writing ".999..." is the same as writing 1 the same way that writing 21/3 is the same as writing 4+3, which is the same as writing 7. Just because one form of nomenclature implies an operation/process doesn't actually mean anything.
Technically. I’ll be back in the morning.