0.999...=1. not accpetable? you're missing meaning of proof!

many people asks why 0.999... is equal to 1. they can't accept it. because they don't understand the definition of limit and the meaning of proof. this video explains the meaning of proof and the definition of limit clearly.
#definitionproof # #why0.999isequalto1 #repeatingdecimals

[pokeali]

Cashier: Your total is £1
Me:ok, here is

[김테스트-tx]

I always enjoy watching your videos. Thank you for providing such great content.

[BertieBoots]

Also, 1/3 does not equal 0, 3333… It’s just an estimate

[BertieBoots]

And if they are the same, why don’t they look the same. 1’s first decimal is 0 but 0, 99…’s is 9. That would not be the case with 2 identical numbers

[BertieBoots]

All proofs I’ve seen do one of 2 things:
1. Say that 1/♾️=0 (like you do)
2. Use infinity when calculating in the way that ♾️+1=♾️ (the common proof: x= 0, 99… 10x= 9, 99.. 9x=9 x=1. The problem is that when you take a decimal times 10, you’ll have one less decimal, which implies one more 0 on the end. I’ll scale down to explain. If x= 0, 999 then 10x= 9, 990x and 9x= 8, 991 and then x=0, 999. You can try this with any amount of nines (even an infinite amount) and it’ll still work this way.)

Both of these methods can’t be used as proof because they are both incorrect.

[BertieBoots]

Questions:
- Prove that 1 is not equal to 0, 99 (that proof can then be used to prove that 1 is not equal to 0)

- What is 1-0, 00…1

- Give an example of to numbers in decimal form with the same value but that look different - not the exact same whole numbers or decimal numbers.

[BertieBoots]

With that logic, you can prove that 1=1, 00….1 and that 1, 00…1=1, 00…2 and so on. That would mean that 1= 1, 00…2 and if you link all these together you can basically get that any real number equals another. Two things aren’t the same just because they’re infinitely close. If they were, that’d mess up everything. 1/infinity (a) • infinity (a)=1 but if I made 1/infinity (a)=0 then that would imply that 0=1 which is incorrect. (The “(a)” implies a specific size of infinity.). To clarify: you can divide (basically) anything into an infinity amount of pieces and if you say that these pieces equate to 0, that would mean that the thing you’re dividing is 0. Example: I created a unit for time and I named it b and b=1s/ ♾️. Time consists of many b’s but if b=0s - that would mean that there is no time. See what I’m saying. This logic simply doesn’t work. Your argument is basically: if two things are infinitely close - they’re the same. If 0, 999…=1, then 1-0, 99…=0 but that’s not the case. The correct answer is that 1-0, 99…=0, 00…1 (though it’s debatable if it has to be a 1 on the end) and that 1 is not equal to 0, 99… (sorry for the long comment 😅)