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Einfach
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Einfach
1,448 posts
Nomad

http://i1124.photobucket.com/albums/l577/gemcrafteinfach/0largestnumber.png

This graph, shown above, is the graph:
y=-1/x
This graph covers the values of all rational numbers (except for 0).

Its derivative (the slope of the tangent line at that particular point) is y=1/x^2, a graph which, for all rational numbers, has a positive y-value, meaning the graph is constantly increasing in value.

As x increases, y constantly increases in value, and y covers all rational numbers. As x approaches infinity, y gets closer and closer to 0. One may logically conclude that 0, therefore, is the largest real number.

One may argue that you are excluding the value x=0, because that cannot be said to have a definitive y-value value at that x-value.. However, look at the derivative, which is 1/x^2. As x approaches 0 in the derivative, y approaches infinity, regardless if you take a positive or negative 0. Therefore, at x=0, the value must be increasing, whatever the corresponding value of y is.

Discuss...

  • 37 Replies
Einfach
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Einfach
1,448 posts
Nomad

This part is where I find fault. There is no logic in your problem that could possibly lead to that conclusion. In fact when you show the equation with the above statement(as opposed to a different statement like it is) you would see that y would have no choice but to get closer to 0 as x increases, however that doesn't translate to 0 being a large number.


1. The derivative is always positive. Thus, it means that the value of y is always increasing in value.
2. As x --> infinity, y --> 0
3. No value of y is repeated. Being a function, no value of x is repeated. There is a corresponding y value for every x value and a corresponding x value for every y value, and x and y cover all real numbers (save 0).
4. Therefore, 0 is the largest real number.
Moe
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Moe
1,714 posts
Blacksmith

I see no reason to go to step 4, there is nothing that leads there.

Sonatavarius
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Sonatavarius
1,322 posts
Farmer

w/ limits you can see where things hypothetically go but never reach... again... where a line crosses the origin is totally different from the value or lack thereof of 0... a co-ordinate system is slightly different from the values of numbers... its plotting things relative to each other rather then just listing things in order based off of value.



save 0 means excluding zero meaning zero's not included meaning zero is not ever graphed meaning zero does not equate to infinity meaning there is an infinitesimally small hole in between the left and right halves of the graph meaning they don't connect meaning zero does not equate to infinity

if you say zero then you're just saying the limit = infinity which does not mean 0 equals infinity... two different concepts

Sonatavarius
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Sonatavarius
1,322 posts
Farmer

for the most recent diagram it is read.... the limit as x approaches 0 = infinity... which i've described above. ....it is not read the two halves curve up indefinitely at 0 therefore 0 = infinity. an asymptote only gets closer and closer to a certain point.... never all the way there. so it never equals it.

aknerd
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aknerd
1,416 posts
Peasant

I see no reason to go to step 4, there is nothing that leads there.


Yep. This isn't a paradox at all, because Einfach just isn't using proper math.

As x increases, y constantly increases in value, and y covers all rational numbers. As x approaches infinity, y gets closer and closer to 0. One may logically conclude that 0, therefore, is the largest real number.


That is not a logical conclusion at all. Really, that's all I need to say. But I'll say more, because I'm bored.

It seems like you're trying to say that because you can construct the number 0 using infinity, 0 = infinity.

But you can't forget that you are taking the inverse of infinity here.

If your function was the monotonically increasing function y=x, and as x approached infinity, y approached 0, then yes, 0 would be the largest number. But the above is a false statement. So... yeah. Inverses...

Furthermore,
Here is your first false statement. It is also your first statement:

]As x increases, y constantly increases in value


Nope. "constantly" implies a continuous function. And this function (nor its derivative!) is continuous at... (dun dun dun) 0.

For future reference: a function is monotonically (the better word for continuously) increasing IFF for all X1 < X2 such that f(X1) < f(X2). Notice that this is not true for the given equation (consider X1 = -1 and X2 = 1). So, your statement is false as well as your conclusion.
lightcrux
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lightcrux
622 posts
Peasant

Nope. "constantly" implies a continuous function. And this function (nor its derivative!) is continuous at... (dun dun dun) 0.

I think you meant discontinuous.

1. The derivative is always positive. Thus, it means that the value of y is always increasing in value.
.....Therefore, 0 is the largest real number.

Steps 1, 2, 3 do not conclusively imply step 4.
Devoidless
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Devoidless
3,675 posts
Jester

...really. This lasted how long? About how 0 is the largest number?

Right. Because the $0 in my shoe is greater than the $150 in my wallet. I'll tell that to my bank next time they try telling my that I have no available funds.
"No, really, zero is the largest number. So if I keep it at zero that means I am rich forever."

Why bother with math (flawed or not) when, you know, a little thing called common sense solves such things.

This thread is the same as those 2+2=5 ones. All just flawed math, tweaking of values or rote rhetoric repeated over and over in attempts to prove that the 'theory' is correct.

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