Simple Math1

[Selivan]

I have two numbers:
A = 1
B = 0.9999999 ... (infinite fraction)
-----------------------------
Question:
Are these two numbers equal or not?

The proof requires a simple knowledge of mathematics ...
Soviet children knew this when they were 12 years old.
-------------------
Do Americans know?

 

[OldLady]

I have two numbers:
A = 1
B = 0.9999999 ... (infinite fraction)
-----------------------------
Question:
Are these two numbers equal or not?

The proof requires a simple knowledge of mathematics ...
Soviet children knew this when they were 12 years old.
-------------------
Do Americans know?

No.

 

[Selivan]

No.

ДА

 

[OldLady]

No.

ДА

 

[Selivan]

Evidence:

B = 0.99999 ... = 0.33333 * 3 = 1/3 * 3 = A
====================
In Mathematics this is called a "rational number"

 

[Wuwei]

I disagree. 0.33333 is not 1/3. The infinite fraction 0.3333333333... will never reach exactly 1/3.

If a set C is defined as the infinite set of rational fractions,
{ 0.9, 0.99, 0.999, 0.9999, etc }
you cannot point to a particular member of that set that is exactly 1.0, so 1.0 lies outside that set.

A is called the supremum of B.
Supremum is defined as the least upper bound.

In order to get into that level of math, you have to understand countable and uncountable infinities.

I learned this stuff in a graduate math class. But for all practical purposes for kids, 0.999999... can be replaced by 1.0.

But, kudos to the Soviet school system which is going into more complex areas of math than American schools.

 

[danielpalos]

I have two numbers:
A = 1
B = 0.9999999 ... (infinite fraction)
-----------------------------
Question:
Are these two numbers equal or not?

The proof requires a simple knowledge of mathematics ...
Soviet children knew this when they were 12 years old.
-------------------
Do Americans know?

They cannot be equal; or we would not need to quibble.

 

[Selivan]

Народ...
Мне это неинтересно.
Я вам дал СТРОГОЕ ДОКАЗАТЕЛЬСТВО.
-----------------

 

[Wuwei]

Народ...
Мне это неинтересно.
Я вам дал СТРОГОЕ ДОКАЗАТЕЛЬСТВО.
-----------------

For the english speaking people:

"People... I'm not interested. I gave you a STRONG EVIDENCE."

 

[Selivan]

"People... I'm not interested. I gave you a STRONG EVIDENCE."

Совершенно верно

 

[Wuwei]

Evidence:

B = 0.99999 ... = 0.33333 * 3 = 1/3 * 3 = A
====================
In Mathematics this is called a "rational number"

Here is another problem with the proof. If you are replacing 0.333333 with it's upper bound, 1/3, you are making the assumption that the upper bound is equivalent to the infinite fraction.
But that is precisely the thing you are trying to prove -- that the infinite fraction 0.99999... can be replaced by it's upper bound, 1.0.

So in short the Soviet school is allowing the kids to assume as true the very thing they are trying to prove.

 

[Selivan]

Тема закрыта.
Учите Математику

 

[Wuwei]

Тема закрыта.
Учите Математику

I disagree. The topic is not closed when faulty mathematics is used in any school system.

 

[danielpalos]

I claim they cannot be equal or there would be no distinction.