Half of a Bucket of Water: Limit or Infinity?

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In summary, the conversation discusses the concept of infinity and its implications on dividing a bucket of water. The conversation also touches on the idea of an entity with infinite capabilities, such as "god," and how that relates to the concept of infinity. Ultimately, the conversation concludes that when it comes to dividing a substance like water, there is a limit to how much it can be split.
  • #1
cragar
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lets say I have a bucket of water with 5 gallons, could I keep pouring half of the weight out for-ever or would I hit a limit like I couldn't split the water molecule to take out half the weight .
 
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  • #2
cragar said:
lets say I have a bucket of water with 5 gallons, could I keep pouring half of the weight out for-ever or would I hit a limit like I couldn't split the water molecule to take out half the weight .

This question is right along the lines of one of my pet peeves... which is... how do you get from 1 to 2 if there is an infinite number of increments between the two qualifiers?

In your case, mind you, there is a slightly more concrete problem in that there are molecules that will eventually be removed from the 5 gallon bucket.

But, let's say you're walking step by step... the distance between each step is infinite... according to incremental measurements... and the point system... help!?
 
  • #3
ok it helps thanks , then you probably would hate the question if god flips a light switch an infinite amount of times is the light on or off .
 
  • #4
In this problem there are two unknowns... god and infinite... can't prove god and can't prove infinite... so any answer will do... like "both".
 
  • #5
When you get down to splitting H2O, you're done splitting "water".

cragar said:
ok it helps thanks , then you probably would hate the question if god flips a light switch an infinite amount of times is the light on or off .

If we're talking about an infinite amount of times being done by an entity who has an infinite amount of time, the flipping never stops.

We're done here.
 

1. What is "Half of a Bucket of Water: Limit or Infinity?"

"Half of a Bucket of Water: Limit or Infinity" is a concept in mathematics that explores the idea of infinite divisions within a finite space. It is often used as an example in calculus and other subjects to help students understand the concept of limits and infinity.

2. How is "Half of a Bucket of Water: Limit or Infinity" relevant to real-world situations?

The concept of "Half of a Bucket of Water: Limit or Infinity" can be applied in various real-world situations, such as measuring the distance traveled by a moving object or calculating the rate of change in a system over time. It is also used in fields like physics, engineering, and economics to solve complex problems.

3. What is the difference between a limit and infinity in relation to "Half of a Bucket of Water"?

A limit refers to the value that a function or sequence approaches as the input or index approaches a specific value, while infinity represents a value that is larger than any finite number. In the context of "Half of a Bucket of Water," the limit refers to the point at which the bucket is divided into an infinite number of halves, while infinity represents the theoretical endpoint of this division, where the amount of water is infinitely small.

4. Why is "Half of a Bucket of Water: Limit or Infinity" important in mathematics?

The concept of "Half of a Bucket of Water: Limit or Infinity" is important in mathematics because it helps to understand the concept of infinity and its relationship to finite quantities. It is also used in various mathematical proofs and equations to solve complex problems and understand the behavior of systems.

5. How can "Half of a Bucket of Water: Limit or Infinity" be visualized?

One way to visualize "Half of a Bucket of Water: Limit or Infinity" is to imagine a bucket being divided into halves repeatedly, with each half becoming smaller and smaller until it approaches an infinitely small amount of water. Another way is to use a graph to represent the relationship between the number of divisions and the size of each division, with the limit being represented by a horizontal line at the endpoint of the graph.

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