Amad27

Hello, If you draw a right triangle, you will clearly see the relation between what you had. If you have an angle suppose t then you can relate it to x to simplify and integrate. Advice: Draw a right triangle and then substitute, you'll see how it works (using the Pythagorean Theorem, ofcourse).

Very true =D Thanks to everyone. But I just didn't want to be left hanging. Which is why I brought up the idea of interpreting word problems as a practice (since the Greeks as you said).

Bump, anyone?...

Hello, In the context of a textbook though, how would you justify that? I remember you saying it has always been that way (since the Ancient Greeks)??

@studiot I have no clue as to how to answer that car question, seems to be very difficult. But now that I think about it, I suppose what the people first said here was correct. That the word problem is supposed to provide you with all information about the existing objects in the scenario Of the "story ." But the only regard to be everyone is that how you would know that the word problem must provide all information to you? Thanks

Yes, I think we are finally getting somewhere I just want to ask one thing here. So as you said it is important to develop a theory etc. Are you agreeing with what I pasted before? Thanks

I was talking about this elsewhere as well, "I'm afraid that without excluding unstated hypotheses and unstated possibilities, we'd never find any satisfying answers, and math could certainly not be applied to any purpose. The list of "what ifs" could persist indefinitely. Answers can be fine-tuned and/or adjusted if we do get more information provided. But we'd never have an answer to fine-tune if we start from the beginning by contemplating what possible complications might exist, and what if this or what if that, and what about...? " What do you think?

So really, Are we making any assumptions when we state that there is no hole in the balloon? What is a mathematical (word problem) assumption??

mmmm.... I researched this, but can you tell me how it works as deductive reasoning? I mean how do you conclude that using deduction?

Hello @Unity+ Can you be willing to tell me something? When you talked a long while ago about the deductive reasoning of "What is in the set, and what is not in set" "It's less of an assumption and more of a conclusion based on deductive reasoning. It's like asking "Well, we may know what is in the set, but then what is not in the set?" You are asking a question that could have an infinite amount of possibilities. Therefore, the logic is not reasonable to follow." Do you still believe this is true? (After this while)?

I am not trolling anyone; otherwise I wouldn't have discussed this. Jeez, I thought a forum would be a good idea to consult with other people, but for some reason it is either some down-voting my posts or telling me that I am a troll. In the context of mathematics, I never troll. Never, never, never ever. I can't believe you thought that.

Hello @ajb. Thank you for advice. In which later studies as you point out will the authors not be telling the truth? also, We have learned to assume the questions aren't trick questions since we were in school. In school teaching, why do you take all information given and not assume it is a trick question? I am talking in formal school education. This is true with my peers as well =) Do you know?

Hello, I think you are right here. Trust is the key in talking I suppose. (Like how I am trusting you ) The question is, should you trust on no basis? In school they teach of these word problems, and they often teach the least complicated way to go about. They never say why.... Thanks @ajb. EDIT ------ They actually teach in school that you implicitly trust the author that he isnt hiding any information. And idea why? OR should I just accept this (no reason)? Also, they implicitly teach you that all information is given, But again, no reason =(

Hello @ajb, When you said, "The questions are usually written so that you use the information in the question only" The whole point of my issue was how do you know that? Again, is it axiomatic or a theory?

True. It would be impossible for the author to (A) Write every assumptions (B) For us to write every assumptions. The only doubt is that, we can never know if the author wants the uncomplicated or the complicated. What a shame. Thanks @ajb, your comments really really really help.

Hello @ajb, I know I am thinking too much. But the reason why is because if I don't see a reason to make such assumptions then it is impossible to interpret a word problem and its assumptions. If the problem says "find the rate at, which ...." Then you can safely judge the problem is solvable (numeric solutions etc). If the problem says "find, if possible, the rate at, which..." then you cannot know if the problem is solvable or not. Really, if a problem is not solvable then you can postulate the existence of holes etc.. On the other hand, if the problem is solvable, then you CANT postulate the existence of holes etc... Aside from that, I know I am over thinking this. How do you suggest I interpret assumptions and word problems WITHOUT over thinking this? Do I just blindly make assumptions (that holes don't exist etc..)? Thanks @ajb. =)

Hello @ajb. Thanks for everything you have done here. Can I ask you one final question? Lets think away from school. What about just general textbooks. For example Ron Larson, Stewart, Apostol etc.. Do you judge the assumptions in the word problems based on context/purpose? Such as, the purpose being to teach mathematics, which can only be done if a problem is solvable? And the context being an informative textbook? What do you say here?

Hello @ajb. This is an unclear topic, isn't it? When you say "enough information will be given," Do you mean this an axiom? Because I see no way to reason this, nor prove this =( Why do you think general high school or college calculus students make such assumptions?

Hello @ajb, So, what do you think the end verdict is here? How should we interpret word problems?

Hello =) I want to share something; I think you might be interested. I think in the end it isn't "solvability," but the way we learned to communicate ever since we were children. Suppose me and you have 4 friends. John, Sam, Dolph, Randy I am holding a party at my house and you ask me who I have invited. I simply respond. "I have invited Dolph and Randy." Immediately, what would you assume? Would you think I invited John or Sam? No right? You would think John & Sam are not invited. I suppose it is the SAME here, as long as you TRUST me that I am not stupid. I suppose we have to trust the author, in that he isn't stupid. =) What do you say?

Hello again, What about on tests or AP Calculus Exams?

Thanks @ajb. Very very helpful. When you said, "It is quite possible that further approximations or simplifying assumptions need to me make for you to actually solve the problem." What do you mean by further simplifying assumptions? So really, at the end, you do need to assume the problem is solvable based on the context =) And then make simplifying assumptions based on the problem being solvable? Correct?

Hello @ajb, thanks a bunch =) I appreciate it. I am hearing two things. (1) Assumptions for simplicity (2) Assumptions for making the problem solvable. I am confused as to, which is correct. =(

Hi, Thanks. This really helped. In the end, in does depend on the context. If the problem is meant to be solved such as in a test or exam correct?

Hi, Apparently, I think you posted before I edited my comment. I think you helped me the best with the simplifying assumptions. Can you confirm my thought, They use simplifying assumptions otherwise nothing would be possible. Also, is it a simplifying assumption that there is no gas leak? Thanks ajb, I owe you big, big, big time.