Can Calculus Prove I Will Reach the End of a Room If I Start Walking?

In summary, the problem statement lacks direction, velocity, and a continuous law of change. If these conditions are met, then the person will eventually reach the other side of the room.
  • #1
wunderkind
12
0
Prove to me mathematically that if I start walking from one end of a room that I will eventually reach the other side. Be sure to include all your formulas!(hint:remember theorems!)
 
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  • #2
The conditions you've provided aren't strong enough. If the speed you're walking at decreases over time fast enough, then it's possible that not even an infinite amount of time would be long enough for you to reach the other side.
 
  • #3
On the other hand, it may be that space is discrete, and that a continuous approximation does eventually break down and stop being useful. (And alas, pragmatic sanction really is the only justification we are left with for our mathematical creations.) There may exist a minimum length scale, below which it is not possible to take steps. In which event, assuming you walk along a "straight line path" from one end of the room to the other, there are only a finite number of steps needed. Then, you will always reach the other side of the room as long as there is not an "infinite" amount of time between any two steps.
 
  • #4
prooving wrong

There is nothing to proove. This problem, at least how it is stated at present, has no true proof.

The problem statement lacks at least the following:

1) Direction in which you are walking.
if you walk along the wall you will never reach the opposite wall.
2) Velocity
velocity that equals zero is also velocity, isn't it? :)
3) the law of changing of the velocity in time.
4) velocity of the opposite wall :)
Consider a train on a railway station! You start walking from the back end to the cockpit ("opposite wall")... in the way, a policeman asks you to leave the train because you have no ticket. The result - you are on the station, train is half a way to [sensored] city... on the way to that city, because of the malfunction in engines the train explodes... there is no train any more... no cockpit... no "opposite wall"... you will never reach it...

:)

i just wonder, what theorems were we supposed to use, to proove your problem as is?
 
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  • #5
in fact i have never made it to the end of my back yard but have started in that direction many times.
 

1. What is calculus and why is it important?

Calculus is a branch of mathematics that deals with the study of change and motion. It is important because it is used to model and analyze real-life situations, such as predicting the path of a moving object or finding the optimal solution to a problem.

2. What makes a calculus problem interesting?

A calculus problem is interesting if it involves a complex concept or requires creative problem-solving techniques. It can also be interesting if it has real-world applications or challenges traditional ways of thinking.

3. How can I improve my skills in solving calculus problems?

The best way to improve your skills in solving calculus problems is to practice regularly. Start with simpler problems and gradually move on to more challenging ones. It is also helpful to review the fundamental principles and concepts of calculus regularly.

4. Can calculus be used in other fields besides mathematics?

Yes, calculus is used in many other fields such as physics, engineering, economics, and even biology. It provides a powerful tool for understanding and analyzing various phenomena and systems in these fields.

5. What are some common mistakes to avoid when solving calculus problems?

Common mistakes to avoid when solving calculus problems include using incorrect formulas, not simplifying expressions, not checking for extraneous solutions, and forgetting to include units in the final answer. It is important to take your time, double-check your work, and be familiar with the concepts and rules of calculus.

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