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Question Number 68493 by H1223 last updated on 11/Sep/19
My question is about the analogical  axiams of the foundation geometry in  mathematocs.  As it Is  a well knowen axum in  geometry  starts from the sefinition of a point which gives  gives the path analogically  to line, plane, and   solids.  Know my truoble  comes at these  axiumes areise from not ne being they  are aziyma ^� but the analogu effect at  giving the definatiom of the solid}  1−Apoimt is a dimenstin less.   mathematixal abstruct.  2− a line is the collextom of points    which has only one dimension.  3− a plane is the collection  of lines   which have onlu?two dimensions   3−a  solid is the collwxripm of plans  which has three dimensions.          Now the first three definationa arsties are mathe  are mathematical ideasor abstruct  while the last mathematical abstruct is real.  ow on earth a real object is formed  from the collextion of unreal planes
$${My}\:{question}\:{is}\:{about}\:{the}\:{analogical} \\ $$$${axiams}\:{of}\:{the}\:{foundation}\:{geometry}\:{in} \\ $$$${mathematocs}. \\ $$$${As}\:{it}\:{Is}\:\:{a}\:{well}\:{knowen}\:{axum}\:{in}\:\:{geometry} \\ $$$${starts}\:{from}\:{the}\:{sefinition}\:{of}\:{a}\:{point}\:{which}\:{gives} \\ $$$${gives}\:{the}\:{path}\:{analogically}\:\:{to}\:{line},\:{plane},\:{and}\: \\ $$$${solids}. \\ $$$${Know}\:{my}\:{truoble}\:\:{comes}\:{at}\:{these} \\ $$$${axiumes}\:{areise}\:{from}\:{not}\:{ne}\:{being}\:{they} \\ $$$${are}\:{aziyma}\bar {\:}{but}\:{the}\:{analogu}\:{effect}\:{at} \\ $$$$\left.{giving}\:{the}\:{definatiom}\:{of}\:{the}\:{solid}\right\} \\ $$$$\mathrm{1}−{Apoimt}\:{is}\:{a}\:{dimenstin}\:{less}. \\ $$$$\:{mathematixal}\:{abstruct}. \\ $$$$\mathrm{2}−\:{a}\:{line}\:{is}\:{the}\:{collextom}\:{of}\:{points} \\ $$$$\:\:{which}\:{has}\:{only}\:{one}\:{dimension}. \\ $$$$\mathrm{3}−\:{a}\:{plane}\:{is}\:{the}\:{collection}\:\:{of}\:{lines}\: \\ $$$${which}\:{have}\:{onlu}?{two}\:{dimensions}\: \\ $$$$\mathrm{3}−{a}\:\:{solid}\:{is}\:{the}\:{collwxripm}\:{of}\:{plans} \\ $$$${which}\:{has}\:{three}\:{dimensions}. \\ $$$$ \\ $$$$\:\:\:\:\:\:{Now}\:{the}\:{first}\:{three}\:{definationa}\:{arsties}\:{are}\:{mathe} \\ $$$${are}\:{mathematical}\:{ideasor}\:{abstruct} \\ $$$${while}\:{the}\:{last}\:{mathematical}\:{abstruct}\:{is}\:{real}. \\ $$$${ow}\:{on}\:{earth}\:{a}\:{real}\:{object}\:{is}\:{formed} \\ $$$${from}\:{the}\:{collextion}\:{of}\:{unreal}\:{planes} \\ $$
Answered by MJS last updated on 12/Sep/19
the R^3  or R×R×R is also an abstract  conception, so where′s the problem???
$$\mathrm{the}\:\mathbb{R}^{\mathrm{3}} \:\mathrm{or}\:\mathbb{R}×\mathbb{R}×\mathbb{R}\:\mathrm{is}\:\mathrm{also}\:\mathrm{an}\:\mathrm{abstract} \\ $$$$\mathrm{conception},\:\mathrm{so}\:\mathrm{where}'\mathrm{s}\:\mathrm{the}\:\mathrm{problem}??? \\ $$

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