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