0.66666… = 1 (in base 7) 

Wouldn't a heptagon (because it has 7 sides) be even better?

@@wyattstevens8574 No, it's like using a triangle to figure out a sum of 1/4^n (Which will become 1/3) Why ? You'll get 6 sides and a central piece that is a smaller version of the entire shape that is 1/7 of the area, making this visual proof possible In a heptagon, what visual representation can be made about such a thing ?

It is the bestagon

Best reference​@@gabekrieck6772

@@gabekrieck6772 true

is this always true?

​@@RandyKing314 yes, always true

​@@cccexestartedwhat about base 1

Oh yeah I forgot about that rule

@@taylormarinescu805 also true

Longer version on my channel (wordless) doesn’t have as much covering it

@@MathVisualProofs I'll have to give it a watch!

If you go into comments and hold the bar near the bottom you can see it without obstruction.

😀

It’s is possible with straightedge and compass. Check my channel for dividing line into 7. The same process works for dividing into 3.

Yes

You mean that your teacher didn't mention sigma meaning sum in passing in your 7th grade math class?

That's why they chose Σ. It's the Greek equivalent of S, and S stands for sum. Furthermore, Π is the Greek equivalent of P, and P stands for product, so Π is used for products.

​@@1leon000 legit had no teacher mention that to me ever before

@@1leon000 Here in east canada it isn't covered at all, even if you take math all the way to senior year

Pretty sure it's manim

manim

It’s a limit

1/n < 1/n-1. Therefore, it's not one below.

@alex_ramjiawan I mean that the sum of thirds gives 1/2, the number as denominator gets smaller, making the portion get larger. 1/5+1/5²+1/5³.....=1/4

wrong the 1st one's ans. is 3/2 And 2nd one's ans. is 6

@@ketanchavda5511 That's incorrect.

yea also cuz 1/9 is 0.111... so 9/9 must be 0.999... but 9/9 is also 1 so 0.999 = 1

@@jepraesidentewhat’s the biggest number before 1?

@@belkYT 1-ε

Are we simply rounding, since we are simply saying 1/infinity is zero?

Well, meaning 0.99999999999… = 1 (in base 10) is true? Well, for bases higher than 10, maybe HEXAdecimal might be 0.FFFFFFFFFFF…….. = 1 (in hexadecimal)

@@chrisrodriguezm13 yeah that works too

S=1+x+x²+x³+... Sx=x+x²+x³+...=S-1 Sx=S-1 Sx-S=1 S(x-1)=1 S=1/(x-1)

Maybe

Yes.

yes

Check my channel for how to break a line into 7 equal pieces with straightedge and compass. Same process works for 3

I have that variation coming at some point :)

Yes, absolutely. Tends to 1 and Is equal to 1 are not the same thing. The former is asymptotic, the latter tangential...

​@@RanjitKonkaryeah

You do. But then if 1/∞ is a number, the only number it can be is 0. If 1/∞ exists, 1/∞=0. Otherwise, 1/∞ doesn't exist, and so you can't have 1/∞ not shaded.

@@xinpingdonohoe3978 huh i thought that 1/ inf would be like how 1/10 would be 0.1 but 1/inf would be 0. Then infinite zeros then one so idk how to describe what I'm thinking but like above 0 but it's infinitely small

@@JaphethThomas-um9gw I get what you mean. Let me explain why it doesn't work. First, there isn't such a thing as an "∞th" decimal place. There's a 1st, and a 2nd, and a 3rd, and so on. There's an nth for every positive integer n. There are infinitely many of these things, because there are infinitely many natural numbers, but every single one is in a finite position. Just like the numbers themselves. 1,2,3,4,5,6,7,... There are ∞ of these, because they never end, but each individual number can be reached by travelling a finite distance. Same with the decimals. Every single bit of the decimal can only be finitely far along, so we can't have a 1 in the ∞th place because there isn't an ∞th place. Also, let's assume it does exist. 0.00...1, so that's 0 point, then ∞ many 0s, then a 1. Call it x. Then 10x=0.00...1 as well. It has ∞-1 0s, but we know ∞-1=∞. Nothing changes. That's the special thing about ∞. For regular numbers, n-1≠n, but for infinity ∞-1=∞. This means we have the same thing. So 10x=x. But then if we subtract x on both sides, 9x=0. Two numbers multiply to 0 if and only if one or both are 0. 9≠0, which means x=0, so 0.00...1=0

It’s on the channel… 😀

Depends on what you mean. 0.3333... won't equal 6.

Yes. Have a couple visualizations on the channel for this.

No. This is a proof that .6666…= 1 (in base 7)

You don't need infinity. Just let 1=0, then you can prove all numbers are equal.

Only if you use it improperly. Limiting processes are well-defined

Base 7. We can only use the digits 0 to 6.

@@xinpingdonohoe3978 thanks chief

Unless a dime=0, or at least a dime

@xinpingdonohoe3978 has to do with percentages. Car is 40k, soda is 1, dime is 0.1. You do the math.

@@blu-birb right, so that's not applicable. Our percentage is 0. We want a change of 0.

@xinpingdonohoe3978 the example is sound. This video claims that X is equivalent to 1, where X=/=1. So that's where I am saying, "depends on accuracy" In the real world, 1-0.1= no soda, but 40k-0.1= yes car. Being that it would be 1/10 of a soda and 1/400,000 of a car.

@@blu-birb but your claim that x≠1 is not correct, so you've either lost soundness or validity.