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Holes in mathematics

american tension

american tension

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This is for people to explore/explain the many holes in the mathematical system. (one of my favorite topics :) )

1. 0.9999 repeating...my personal favorite, a repeating decimal that cannot be expressed as a fraction. my 8th grade math teacher, when asked said that it was so close to 1 that it just was 1..bs >_<

2. 0 = X divide either side by X and you get 0 = 1

also, i'd have to get the exact equation from him, but my friend found an equation that starts out logical and ends in all numbers being equal lol
 
american tension said:
This is for people to explore/explain the many holes in the mathematical system. (one of my favorite topics :) )

1. 0.9999 repeating...my personal favorite, a repeating decimal that cannot be expressed as a fraction. my 8th grade math teacher, when asked said that it was so close to 1 that it just was 1..bs >_<

2. 0 = X divide either side by X and you get 0 = 1

also, i'd have to get the exact equation from him, but my friend found an equation that starts out logical and ends in all numbers being equal lol
Click to expand...

0 cannot be divided by anything, because it is nothing. Try taking no apples and giving them to your friends.

Just because a number can't be a fraction, doesn't mean there is a loop in mathematics. And it is possible: 0.9999999.../1.
Also some people consider 0.9999... as 1 because it is so close to it. This doesn't mean it is 1.

and in your last sentance, I think you mean the numbers on both sides are illogical, and then end up the same. If something is logical, then is the same on both sides, it's still logical.
 
I don't really understand #2. 0 = X is the same as X = 0 meaning X is equal to 0 not 1.
 
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Cymru said:
Yeh I've seen that as well. Can't explain it though...
This is different to the thread owners one though.
Click to expand...

Well its easy to understand.

Imagine you are walking somewhere, and every step you divide your stride by 10. So if you step a meter in the first stride the you step only 10 cm in the next step, then only 1 cm in the next step, then only one millimeter in the next step then only one tenth of a millimeter, etc.

If you took infinite steps (never stopped) in this fashion its mathematically predictable where you will end up -- eventually the amount you were moving forward by would be so small as to be no different to not moving at all.

We call these limits. Because you can't actually take infinite steps, you will never get to the limit of the function, but you will get closer and closer the longer you stay at it. So the concept is that you will reach the limit of the function at infinity -- which is impossible to get to, but mathematically useful.
 
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The amount of fractions contained between two integers is infinite. Simply because the denominator contains an integer.
 
Cymru said:
0 cannot be divided by anything, because it is nothing. Try taking no apples and giving them to your friends.

Just because a number can't be a fraction, doesn't mean there is a loop in mathematics. And it is possible: 0.9999999.../1.
Also some people consider 0.9999... as 1 because it is so close to it. This doesn't mean it is 1.

and in your last sentance, I think you mean the numbers on both sides are illogical, and then end up the same. If something is logical, then is the same on both sides, it's still logical.
Click to expand...
Or, you could just express it as a fraction.

.111111111 = 1/9
.222222222 = 2/9
.999999999 = 9/9 = 1

Tada!

nothing special about either equations, dividing by 0 (when X = 0 ) will give you a no solution answer. Multiplying by X on both sides may give you extraneous answers, as in the 1 = 2 proof.
 
Sythe said:
Well its easy to understand.

Imagine you are walking somewhere, and every step you divide your stride by 10. So if you step a meter in the first stride the you step only 10 cm in the next step, then only 1 cm in the next step, then only one millimeter in the next step then only one tenth of a millimeter, etc.

If you took infinite steps (never stopped) in this fashion its mathematically predictable where you will end up -- eventually the amount you were moving forward by would be so small as to be no different to not moving at all.

We call these limits. Because you can't actually take infinite steps, you will never get to the limit of the function, but you will get closer and closer the longer you stay at it. So the concept is that you will reach the limit of the function at infinity -- which is impossible to get to, but mathematically useful.
Click to expand...

Yeh I understand it, but it doesn't make sense that it makes sense :P
It's cool. Most of the other ones people show us are ones where you devide by 0 or 0 devide by X.
 
Cymru said:
0 cannot be divided by anything, because it is nothing. Try taking no apples and giving them to your friends.

Just because a number can't be a fraction, doesn't mean there is a loop in mathematics. And it is possible: 0.9999999.../1.
Also some people consider 0.9999... as 1 because it is so close to it. This doesn't mean it is 1.

and in your last sentance, I think you mean the numbers on both sides are illogical, and then end up the same. If something is logical, then is the same on both sides, it's still logical.
Click to expand...

u got it rong in ure first bit...0 can be divided, thats why it works when u put it in a calculator...and i didnt say x = 1 (other people)
i said x/x is 1...even if u wanna change it u can make x =2, so that x - 2 = 0 and divide either side by the phrase x-2 and still get 1=0, and tbh u rlly can divide variablees, in any case you get conflicting rules of math, because x/x = 1 but x/0= undefined, so if x=0 then in essence u come out with 1 = undefined >_<

and as for ur explanation of 9 repeating, every other rational number can be expressed as a faction with no decimal....if you put pi over 1, does that make it rational? not exactly.

and a lot of u are making equations to make 0.9999... equal 1, but that doesnt make any sense in it's own right, being 0.999... < 1

and my friend's proof starts with variables and ends with 1=2, which can be continued just by adding/multiplying etc. either side
 
american tension said:
and a lot of u are making equations to make 0.9999... equal 1, but that doesnt make any sense in it's own right, being 0.999... < 1
Click to expand...


.111111111 = 1/9
.222222222 = 2/9
.999999999 = 9/9 = 1

YOU CAN EXPRESS IT AS A FRACTION IF YOU USE YOUR HEAD A BIT>>>
 
my head hurts.

our math system is okay i mean we don't need it to be perfect as long as 2 + 2 = 4.
 
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american tension said:
1. 0.9999 repeating...my personal favorite, a repeating decimal that cannot be expressed as a fraction. my 8th grade math teacher, when asked said that it was so close to 1 that it just was 1..bs >_<
Click to expand...
What Sythe said a few posts up.

american tension said:
2. 0 = X divide either side by X and you get 0 = 1
Click to expand...
...

Because X = 0, dividing by X is dividing by zero. You cannot divide by zero, therefore, you cannot divide by X because X = 0. Fail.

american tension said:
also, i'd have to get the exact equation from him, but my friend found an equation that starts out logical and ends in all numbers being equal lol
Click to expand...
If it's that 1 = 2 thing, that's a fallacy as well - it has a divide by zero error somewhere in the chain of steps.
 
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