September 25th, 2018, 11:30 AM  #21  
Senior Member Joined: Oct 2009 Posts: 544 Thanks: 174  Quote:
You seriously are going to attack the use of "infinity" in mathematics, and then go on define a point as something of INFINITESIMAL length? Are you serious right now? Really?  
September 25th, 2018, 11:33 AM  #22  
Senior Member Joined: Oct 2009 Posts: 544 Thanks: 174  Quote:
Take a point according to your definition. It has an infinitesimal radius d. So what is 1/d? What does that equal according to you?  
September 25th, 2018, 11:42 AM  #23 
Senior Member Joined: Jun 2018 From: UK Posts: 103 Thanks: 1 
1/d where d is an infinitesimal is an expression that tends to but never actually reaches infinity. So at best we could write 1/d ~ oo (because actual infinity does not exist).

September 25th, 2018, 12:12 PM  #24  
Senior Member Joined: Oct 2009 Posts: 544 Thanks: 174  Quote:
So in classical geometry that everybody is doing, we have circles of a definite radius, say 2 or 3 or 10. In your geometry, you say that al of that is very confusing, and you instead replace it with circles whose radius aren't like numbers anymore, but expressions that tend to infinity but not reach it? How are you going to draw such a circle with a 'radius that tends to infinity and not reach it'? How are you going to show a picture of it in textbooks? Say what you want about our flawed math system, but when we talk about a circle with radius 1, we can actually DRAW it.  
September 25th, 2018, 12:14 PM  #25 
Senior Member Joined: Oct 2009 Posts: 544 Thanks: 174 
Also, let y = 1/d be your number that tends to infinty but not reaches it. What is y+1? Is y+1>y? Is y+1=y? 
September 25th, 2018, 12:14 PM  #26 
Senior Member Joined: Aug 2017 From: United Kingdom Posts: 264 Thanks: 79 Math Focus: Algebraic Number Theory, Arithmetic Geometry  
September 25th, 2018, 12:22 PM  #27 
Senior Member Joined: Oct 2009 Posts: 544 Thanks: 174 
Here is a fun one: If x is a real number such that its integer part is even, then we set f(x) = 0. If x is a real number such that its integer part is odd, we set f(x) = 1. Clearly, we have like f(3.14)=1, since the integer part is 3, which is odd. Or we have like f(6.4) = 0 since the integer part is 6, which is even. So, clearly the integer part of d is 0, so f(d) = 0. What is f(1/d)? Or what is sin(1/d)? Is it positive or negative? 0? 
September 25th, 2018, 12:34 PM  #28  
Senior Member Joined: Jun 2018 From: UK Posts: 103 Thanks: 1  Quote:
Sin(1/d) is also likewise dependant. Last edited by Devans99; September 25th, 2018 at 12:41 PM.  
September 25th, 2018, 12:40 PM  #29 
Senior Member Joined: Oct 2009 Posts: 544 Thanks: 174  
September 25th, 2018, 12:41 PM  #30 
Senior Member Joined: Oct 2009 Posts: 544 Thanks: 174 
Anyway is 1/d bigger than every number? Is (1/d) + 1 > (1/d)? 

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‘point’, contradictory, definition, geometry 
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