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July 20th, 2018, 04:14 AM   #11
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Quote:
 Originally Posted by Matt C That isn't math rules, . . .
Counting is basic arithmetic, and uses simple logical principles. Your assertion that something is nonsense doesn't mean that it's nonsense, only that you've posted the assertion, especially when you've not posted a detailed logical argument to support the assertion.

If objects are counted and the count reaches six, it doesn't follow that there are six distinct objects unless each object in the count has been counted just once.

Quote:
 Originally Posted by Monox D. I-Fly . . . but you misinterpret area as half the perimeter instead.
Perhaps, but the area concept wasn't explicitly mentioned. For a theoretical disk having radius 1, its area is $\pi$, which is half its perimeter.

 July 20th, 2018, 06:32 AM #12 Member   Joined: Oct 2017 From: Japan Posts: 62 Thanks: 3 Describing a rectangular section with dots is misleading, if you use segments instead, or you place the dots in the middle of hypothetical segments, there is no fallacy in the problem.
 July 20th, 2018, 06:54 AM #13 Banned Camp   Joined: Jul 2018 From: beverly hills Posts: 15 Thanks: 0 How any number of objects is counted does not change how many objects there actually are. 5 objects cannot ever become 6 objects without actually increasing the number of objects, from 5 to 6. The fact is that the math rules prove that all anyone here is doing is making things up to get the math to fit how they want it to work, instead of actually using the math and its rules to solve the problem. The problem is and always will be addition, never multiplication. Last edited by skipjack; July 31st, 2018 at 12:34 AM.
July 20th, 2018, 11:39 AM   #14
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There are five dots (3 + 2 or 2 + 3, as you observed) in your first diagram and six dots (3 + 3) in your second diagram. They are different diagrams that have a different number of dots and haven't been proved to correspond to the same rectangle.

To use "real rules", you also need clear definitions of the terms you use... I can understand the "width" and "height" concepts you mentioned, but what exactly did you mean by "depth"?

The dots you used were shown on two parts ("top" and "left side") of the perimeter of a rectangle in each diagram. The dots are positioned differently in the two diagrams and the rectangles haven't been shown to be identical and don't appear to be identical, so there is no contradiction involved in relation to the number of dots used in each diagram.

Is there a mathematical difference in meaning between the terms "unit" and "dot" that we've been using? I used "dot" because your diagrams consist of dots. For clarity, is there any mathematical reason why "dot" shouldn't be used throughout instead of "unit"?

Quote:
 Originally Posted by Matt C You cannot have both 3 on top and 3 on the bottom with a total of only 5 actual units.
Why is that relevant, given that neither of your diagrams has 3 on top and 3 on the bottom? Your second diagram contained 6 dots, 3 along the top, and a separate 3 along the left side. There's nothing to suggest that this diagram should be considered to have "only 5 actual units". Is there any mathematical difference in meaning between "actual units" and "dots", or between "actual units" and "units"?

[Aside by Denis]: Matt my boy, whatzit you've been smoking?

July 20th, 2018, 05:13 PM   #16
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Quote:
 Originally Posted by Matt C In addition, the number five is 5, there isn't any changing that no matter what you try and do to it, how it's arranged, and or how it's counted, in the end it's still 5.
For suitable values of 5, of course.

 July 20th, 2018, 05:33 PM #17 Senior Member   Joined: May 2016 From: USA Posts: 1,306 Thanks: 549 Arguing with someone who is determined to remain ignorant is pointless. Within the non-negative integers, here is a definition of multiplication $m \times n = 0 \text { if } n = 0 \text { and } \\ m \times n = m + m \times (n - 1) \text { if } n > 0.$ $\text {THUS } 3 \times 0 = 0 \implies 3 \times 1 = 3 + 0 = 3 \implies 3 \times 2 = 3 + 3 = 6.$ Because the OP almost certainly could not have given a definition of multiplication before reading this post, nothing the OP says about multiplication is worth paying attention to. He may think that buying 3 hamburgers costing 4.99 each means he must pay 7.99, but he won't get 3 burgers for that sum. There is no reason to discuss multiplication with someone who can't go to McDonalds without an adult guardian. In short, DON'T FEED THE TROLLS. Thanks from Sebastian Garth and topsquark
July 20th, 2018, 05:51 PM   #18
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Quote:
 Originally Posted by Matt C Which brings me to the whole problem with math in general. You cannot teach someone basic addition/multiplication, say here are the rules and this is how it works, then later on remove that from the problem and totally go against the basic foundation of what they were just taught on how the system works.
On the level that you appear to be working on this is undoubtedly true. But advanced Mathematics can make serious use of generalizing these ideas and some very applicable results ensue. Advanced Physics would be nowhere unless we can use this material. (Your computer, for example, is made by knowledge of these "extended" Algebraic operations.)

-Dan

July 20th, 2018, 06:32 PM   #19
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Quote:
 Originally Posted by topsquark On the level that you appear to be working on this is undoubtedly true. But advanced Mathematics can make serious use of generalizing these ideas and some very applicable results ensue. Advanced Physics would be nowhere unless we can use this material. (Your computer, for example, is made by knowledge of these "extended" Algebraic operations.) -Dan
Except the basic math rules CANNOT EVER BE REMOVED from anything, because the basics are what make the way it is and possible, so when you say things like "Except Advanced Math" you're removing basic math rules from math, and making up crap that goes against math in general which makes everything you just said totally incorrect and false.

________________________________________
As for this:
Quote:
 Originally Posted by JeffM1 Within the non-negative integers, here is a definition of multiplication. $m \times n = 0 \text { if } n = 0 \text { and } \\ m \times n = m + m \times (n - 1) \text { if } n > 0.$ $\text {THUS } 3 \times 0 = 0 \implies 3 \times 1 = 3 + 0 = 3 \implies 3 \times 2 = 3 + 3 = 6.$
One thing you failed to include is that multiplication IS IMPOSSIBLE without addition, because multiplication IS ADDITION, and cannot be removed from the equation, and so the only thing you've accomplished with this little rant of yours, is verify exactly what I said right from the beginning.
You're not using math, but manipulation tactics to force math to work in a manner the basics will not and do not ever allow.

Furthermore, that little set up you did, does not allow a diagram that has only 5 things to count, to somehow magically now equal 6. In order to get the number 6 from that diagram, then The diagram itself literally requires 6 actual things to count.

Last edited by Matt C; July 20th, 2018 at 07:02 PM.

July 20th, 2018, 06:45 PM   #20
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Quote:
 Originally Posted by Matt C Except the basic math rules CANNOT EVER BE REMOVED from anything, because the basics are what make the way it is and possible, so when you say things like "Except Advanced Math" you're removing basic math rules from math, and making up crap that goes against math in general which makes everything you just said totally incorrect and false.
You know there's an answer to that.

In math, we study the logical consequences of sets of rules. When we study the counting numbers 1, 2, 3, ... we use one set of rules. When we study the real numbers we use a different set of rules. Whatever area of math we're working in, there's a set of rules and we work out the consequences of those rules.

But mathematicians are not bound to any particular set of rules. In fact the rules are historically contingent. In the Middle ages people didn't believe in negative numbers, or zero, or really crazy things like the square root of -1. Over the years, all these things have become a normal part of everyday math.

So math is a historically contingent human activity. It seems as if you are comparing it to some imaginary perfection and saying math isn't perfect. Well, there's math and there's math. We might mean math as in God's math, the Platonic perfection of idealized math, in which every question has an answer; even if Gödel showed that there might not be a proof from a given system of rules.

Maybe God's math exists or maybe there is no such thing. Maybe math is nothing more than a formal game played with marks on paper. Who knows?

But compare God's math, which we can imagine existing whether or not it actually exists; to human math. God's math is eternal; and human math is what's trendy in the math journals.

So you have to be careful which math you're against. Or perhaps you're just unhappy that the true math, God's math is perfect and human math isn't.

I have no idea if any of this is helpful, they're just some thoughts I had on skimming your posts. Can you say briefly, sentence or two, why you are against math?

Last edited by skipjack; July 20th, 2018 at 11:21 PM.

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