A -ve number greater than infinity?

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In summary: So, as the x value approaches 0, the y value (or output) gets closer and closer to infinity. However, it will never reach infinity because it is asymptotic to the x-axis. Therefore, 5/0 does not equal infinity, but the limit of 5/x as x approaches 0 is infinity. In summary, as the denominator in the equation 5/x decreases, the resulting answer increases. However, this pattern does not apply to all numbers, as seen when substituting -1 as the denominator. The curve 5/x, or a rectangular hyperbola, is an asymptotic curve that approaches but never reaches infinity as the denominator approaches 0. Therefore, it is incorrect to say that -
  • #1
AlbertEinstein
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Please follow the following arguments.
5/3=1.66
5/2=2.5
5/1=5
5/0.5=10
...
...
5/0=infinity
and then 5/(-1)= -5
What you see? As the denominator is decreased the right hand side answer increases. The denominator becomes 3 then 2,then 1, then 0,then -1 ; and the answer increases, therefore -5 must be grater than infinity.
Where's the flaw. Please illustrate.
 
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  • #3
AlbertEinstein said:
and the answer increases, therefore -5 must be grater than infinity.
Where's the flaw. Please illustrate.

In assuming that because for some set of values f(x) is increasing it is always increasing.
 
  • #4
Mainly, your answer doesn't work because 5 is a prime number.
 
  • #5
As one divides by smaller and smaller numbers, the output figure approaches but does not reach infinity, no?
 
  • #6
Depends on your notion of smallness.
 
  • #7
Please follow the following arguments.

5=5
4=4
3=3
2=2
1=1
0=0
-1=-1

What do you see? As the left hand side decreases, the right hand side is greater than or equal to zero. Therefore, -1 must be greater than or equal to zero.

Ja?

Just because a property holds true for a certain range of numbers, it doesn't mean the pattern will follow for numbers outside that range. That's the flaw.
 
  • #8
AKG said:
Mainly, your answer doesn't work because 5 is a prime number.
:rofl: :rofl: That's funny.
 
  • #9
Gokul43201 said:
:rofl: :rofl: That's funny.

It is? :confused:
 
  • #10
Ya, its funny because AKG's answer isn't right.
ja ja
 
  • #11
5/0 does not equal infinity. The limit of 5/x as x approaches 0 equals inifinty.
 
  • #12
daveb said:
5/0 does not equal infinity. The limit of 5/x as x approaches 0 equals inifinty.
In absolute value, yes. But else you have to mind the sign, depending on whether you're approaching 0 from the left or right, you get -inf resp. +inf.
 
  • #13
I don't see how you can say that -1 is greater than or equal to 0. I might be horribly wrong but what I think you're doing is just equating numbers & two equal numbers are always equal .. under no circumstances can be greater than or equal to.

Look at this order:

1=1
9=9
8=8
-1=-1

Don't you see?
 
  • #14
Albert:

Please follow the following arguments.
(x^2=y)
3^2=9
2^2=4
1^2=1
0^2=0
-1^2=1

What you see? As the x value is decreased, the y value (right hand side answer) decreases. The x value becomes 3 then 2,then 1, then 0,then -1 ; and the answer (y) decreases, therefore 1 must be less than zero.

Now where's the flaw?


(Hint: the only flaw is the conclusion that a given function must result in a straight and continuous line.)
 
Last edited:
  • #15
Okay...let me try to hit this topic.
Graphing 5/x you will have a line that going from negative infinity to positive infinity it ALWAYS DECREASES. it never increases. However, it starts out negative and ends up positive.

Lesson learned today: Don't mess with the division by zero.
 
  • #16
Robokapp said:
Okay...let me try to hit this topic.
Graphing 5/x you will have a line that going from negative infinity to positive infinity it ALWAYS DECREASES. it never increases. However, it starts out negative and ends up positive.

Lesson learned today: Don't mess with the division by zero.

No you do not have a line. You have a hyperbola in the first and third quandrants of the cartesian plane.
 
  • #17
Here am a graph of 1/x.
http://www.mathsrevision.net/gcse/1overx.gif
5/x follows the same pattern.
 
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What does it mean for a number to be negative and greater than infinity?

When we think of infinity, we often think of a number that is larger than any other number. However, negative numbers are smaller than zero, so how can a negative number be greater than infinity? In mathematics, infinity is not a specific number, but rather a concept that represents the idea of endlessness. Therefore, a negative number that is greater than infinity simply means that it is smaller than zero, but not bound by any specific number.

Can negative numbers be greater than positive infinity?

As mentioned before, infinity is not a specific number, but a concept. In mathematics, there is no positive or negative infinity. Therefore, negative numbers cannot be greater than positive infinity because infinity itself is not a number that can be compared to other numbers.

Is there a largest negative number?

In theory, there is no largest negative number. This is because there is always a number that is smaller than any given negative number. For example, -999 is smaller than -998, and -1000 is smaller than -999. This pattern continues infinitely, so there is no largest negative number.

How do we represent a negative number greater than infinity?

In mathematics, we use a notation called "limit" to represent a number that approaches infinity. For example, if we say the limit of a number x is infinity, it means that x is getting closer and closer to infinity but never actually reaches it. Similarly, we can use limit notation to represent a negative number that is greater than infinity, such as the limit of x as x approaches negative infinity.

What is the practical application of negative numbers greater than infinity?

Negative numbers greater than infinity are often used in advanced mathematics, such as calculus and complex analysis. In these fields, the concept of infinity is used to solve complex equations and understand the behavior of functions. By understanding how negative numbers can be greater than infinity, we can better understand and solve these complex problems.

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