0.9999... equals 1.0000....

[UltraBudgie]

numbers that repeat to infinity are weird.  let x equal 0.9999...

x = 0.9999...

then multiply each side by 10:

10x = (10 * 0.9999...)
10x = 9.9999...

then subtract x from each side:

(10x - x) = (9.9999... - x)
9x = (9.9999... - 0.9999...)
9x = 9.0000...

then divide each side by 9:

(9x / 9) = (9.0000... / 9)
x = 1.0000...

therefore 0.9999... = 1.0000...

[IdeomotorPrisoner]

I love crazy math counterintuitions. I never went past trig/statistics, but looked this up to look smart. E⁰, (cos)0, and (tan)45 also equal 1! 

I think the reason .9999... = 1 or 9.9999... equals 10 is because of an infinity/integer paradox where there is no number, no matter how small that can be inserted between the two numbers to equal the next whole number.  

.9999 + .0001 = 1 but the infinitely repeating never has a place for the eventual .0001.

[Quantum12]

I love crazy math counterintuitions. I never went past trig/statistics, but looked this up to look smart. E⁰, (cos)0, and (tan)45 also equal 1! 

I think the reason .9999 = 1 or 9.9999 equals 10 is because of an infinity/integer paradox where there is no number, no matter how small that can be inserted between the two numbers to equal the next whole number.

This too?

[UltraBudgie]

This too?

No, that's just proves you've invented time travel.

[IdeomotorPrisoner]

No. That's revenue driven. That's actually 9/10 of a cent. A way to make slightly more. It equals 90%. 

I prefer Donny's Discount Gas for this reason.

[Quantum12]

No, that's just proves you've invented time travel.

Thomas Jefferson wrote it in the constitution. lol.

[Quantum12]

No. That's revenue driven. That's actually 9/10 of a cent. A way to make slightly more. It equals 90%. 

I prefer Donny's Discount Gas for this reason.

Haha! Way better!

[UltraBudgie]

E⁰

This is obviously correct and smart because it has those tiny numbers that scientists use.

[IdeomotorPrisoner]

I like reading about things like string theory with the ultra technical wiki pages.

Love these. They look pretty and smart. 



Of course. It's all so apparent now! Like an atheist reading the Gideons hotel Bible to make fun of endless pages of cubit measurements..

I got as far as the sigma notation symbol starting to get used in statistics. The E looking thing was like a super equal sign.

I respect those that could understand that string of gibberish. Like the Good Will Hunting surfer that came up with M Theory. The super genius that looks at that and says, "Obviously, we need to add another super-dimensional plane for the oscillating parameters." 

Something like that. I find embracing ignorance makes you feel less daunted by the movie genius math proofs.