My Math Forum Is the Is definition of a ‘point’ in geometry contradictory?

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September 29th, 2018, 11:33 AM   #71
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Quote:
 Originally Posted by Devans99 If you appreciated the history you would not have made that remark. Cantor included Actual Infinity in set theory because he believed god was infinite.
And Kronecker opposed infinity also for religious reasons.

 September 29th, 2018, 11:34 AM #72 Senior Member   Joined: Oct 2009 Posts: 864 Thanks: 328 And Newton came up with his classical mechanics also for very biblical reasons. You're opposed to that too?
September 29th, 2018, 12:13 PM   #73
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Quote:
 Originally Posted by Devans99 If you appreciated the history you would not have made that remark. Cantor included Actual Infinity in set theory because he believed god was infinite.
You don't appreciate very much about about mathematics at all. Almost all mathematicians of any note have had a strong religious belief.

Last edited by v8archie; September 29th, 2018 at 01:00 PM.

 September 29th, 2018, 12:30 PM #74 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond Using your logic and improving the technique we have $$\lim_{x\to0^+}\frac{C}{x}=\infty$$ so there are an infinite number of points on a circle. Now what do you say?
September 30th, 2018, 03:39 AM   #75
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 Originally Posted by greg1313 Using your logic and improving the technique we have $$\lim_{x\to0^+}\frac{C}{x}=\infty$$ so there are an infinite number of points on a circle. Now what do you say?
The whole point of a limit should be that it tends to but does not ever reach Actual Infinity because that is undefined mathematically. If you evaluate your limit with x=0 it’s undefined because it’s a divide by zero error...

September 30th, 2018, 03:45 AM   #76
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 Originally Posted by Devans99 The whole point of a limit should be that it tends to but does not ever reach Actual Infinity because that is undefined mathematically. If you evaluate your limit with x=0 it’s undefined because it’s a divide by zero error...
Oh my god, dude, learn what a limit is before you comment nonsense.

September 30th, 2018, 03:47 AM   #77
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Quote:
 Originally Posted by Devans99 The whole point of a limit should be that it tends to but does not ever reach Actual Infinity because that is undefined mathematically. If you evaluate your limit with x=0 it’s undefined because it’s a divide by zero error...
The issue, again, is that you have no idea what limits are. It's not hard to look up a definition - if the definition seems confusing, we'll be more than happy to explain and help you understand.

 September 30th, 2018, 09:57 AM #78 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond Nothing can ever reach "Actual infinity" - that's what makes infinity what it is. With the expression C/x, we can make its value as large as we like by making x sufficiently small. The result is without bound. In notation, this is $\infty$.
 October 2nd, 2018, 08:48 AM #79 Member   Joined: Oct 2018 From: Netherlands Posts: 39 Thanks: 3 If a point had "length" then it would have to be measured from A to B. If that length is >0 then A and B are different and therefore 2 points, not just 1. Whatever the consequence, you have to accept that a single point has 0 length. It is quite similar to accepting that 0 is an existing number even though it is not an existing quantity. The Roman empire never came to that understanding, so you are in good company Thanks from studiot
October 2nd, 2018, 10:56 AM   #80
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 Originally Posted by Arisktotle If a point had "length" then it would have to be measured from A to B. If that length is >0 then A and B are different and therefore 2 points, not just 1. Whatever the consequence, you have to accept that a single point has 0 length. It is quite similar to accepting that 0 is an existing number even though it is not an existing quantity. The Roman empire never came to that understanding, so you are in good company
Yeah simply put but well put.

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