July 20th, 2018, 03:14 AM  #11 
Global Moderator Joined: Dec 2006 Posts: 20,919 Thanks: 2203  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. 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, 05:32 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, 05:54 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 30th, 2018 at 11:34 PM. 
July 20th, 2018, 10:39 AM  #14  
Global Moderator Joined: Dec 2006 Posts: 20,919 Thanks: 2203 
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:
[Aside by Denis]: Matt my boy, whatzit you've been smoking?  
July 20th, 2018, 04:00 PM  #15 
Banned Camp Joined: Jul 2018 From: beverly hills Posts: 15 Thanks: 0 
The original point to this topic has gotten lost which is to explain/show the exact reason why people who say they cannot do math, cannot do it. Instead people are too hung up with cramming an incorrect, corrupted, very flawed system into existence, and then claim it's fine. When people are taught basic math (Basic meaning addition, subtraction, multiplication, division) they're taught very basic concepts on what make those the way they are. Which is why I used addition and multiplication. 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. Multiplication is just a shortcut to adding, so in order for 2 and 3 to be 6 then it requires 6 actual things to be counted which is either two groups of 3, or three groups of 2, which again is because there are 6 actual things present to do that with, and multiplication tells you it's impossible to get 6 without there actually being 6 actual things to put together. Same is revered, you cannot make 6 items become 5 without actually removing one of the items itself. And that brings me to this topic, People replying in this thread are failing on all ends to put the basic addition and multiplication to practice, because everyone is totally ignoring THE FACT THAT THERE ARE ONLY 5 THINGS PRESENT (in the first diagram) and focusing on the size and what things are being called and manipulating the counting process. The term isn't relevant and neither is the size of the area, along with whatever other manipulation tactic people want to try and say and use. The ONLY FACTOR THAT MATTERS IS how many units are present which is where the basic addition and multiplication gets used. 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. Under the addition and multiplication rules you're taught as the basics and how those work, then that means the number 6 CANNOT be obtained from the first diagram no matter what is attempted. Counting one 2 unit times IS NOT MATH, it's nothing but a manipulation tactic that fails to actually apply the rules of basic addition and multiplication. but of course it appears to be possible, that's because it's just been manipulated, however when you revert back to the actual math itself, that manipulation not possible because the math system itself will literally prevent 5 units from ever becoming 6, without adding one more unit itself which now makes a total of 6 things present to count from. I can count 5 things any way I choose which allows me to create and come up with any number I want, but in the end it's not relevant what I choose to do, the basic addition and multiplication rules will literally prevent me from having any number except 5, just because I manipulated the counting process, DOES NOT CHANGE THE FACT THAT THERE ARE STILL ONLY 5 THINGS TO COUNT. So unless there are 6 actual things to count, then no one in the world is ever going to actually say that the first diagram can amount to any number except 5 because of counting manipulation. Basic addition and multiplication work a certain way, manipulate a counting process does not get around that. Rational and sane human being's, are not going to waste time with that type of sheer stupidity and utter nonsense. Nor are they ever going to accept it either. So you've already lost them and now the person is never going to be able to do math. What really gets me is how all anyone does is blame the person for not wanting to learn or being stubborn, instead of accepting that the people manipulating counting to get around and avoid having to use basic math So if math is an absolute, then that means the first diagram because there are only 5 things to count and thus cannot be anything but 5 which makes it an addition problem (Not multiplication) Multiplication would require there to be 6 actual things to count, and not just some counting manipulation tactic. So in diagram one, if there are only 5 things to count then the math system itself is telling you that the answer is 5, manipulation counting can create any number it wants to, but the number manipulation counting comes up with is 100% wrong because the basic math system itself, says so. And that's all there is too it. Last edited by Matt C; July 20th, 2018 at 04:15 PM. 
July 20th, 2018, 04:13 PM  #16 
Senior Member Joined: Aug 2012 Posts: 2,355 Thanks: 737  
July 20th, 2018, 04:33 PM  #17 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 
Arguing with someone who is determined to remain ignorant is pointless. Within the nonnegative 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. 
July 20th, 2018, 04:51 PM  #18  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,256 Thanks: 926 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
July 20th, 2018, 05:32 PM  #19  
Banned Camp Joined: Jul 2018 From: beverly hills Posts: 15 Thanks: 0  Quote:
________________________________________ As for this: Quote:
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 06:02 PM.  
July 20th, 2018, 05:45 PM  #20  
Senior Member Joined: Aug 2012 Posts: 2,355 Thanks: 737  Quote:
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 GĂ¶del 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 10:21 PM.  

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