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is-zero-a-natural-number-0-N-

Question Number 114807 by Eric002 last updated on 21/Sep/20 $${is}\:{zero}\:{a}\:{natural}\:{number}\:\mathrm{0}\in\mathbb{N}? \\ $$ Commented by MJS_new last updated on 21/Sep/20 $$\mathrm{there}\:\mathrm{seem}\:\mathrm{to}\:\mathrm{be}\:\mathrm{two}\:\mathrm{different}\:\mathrm{definitions} \\ $$$$\mathrm{of}\:\mathbb{N},\:\mathrm{both}\:\mathrm{are}\:\mathrm{in}\:\mathrm{use}…\:\mathrm{confusion}… \\ $$$$\mathrm{old}\:\mathrm{definition}\:\mathbb{N}=\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:…\right\};\:\mathbb{N}\cup\left\{\mathrm{0}\right\}=\mathbb{N}_{\mathrm{0}} \\…

Question-114803

Question Number 114803 by Eric002 last updated on 21/Sep/20 Commented by Eric002 last updated on 21/Sep/20 $${the}\:{white}\:{square}\:{in}\:{the}\:{drawing}\:{below} \\ $$$${is}\:{located}\:{in}\:{the}\:{center}\:{of}\:{the}\:{grey}\:{rectangle} \\ $$$${and}\:{has}\:{a}\:{surface}\:{area}\:{of}\:{A}.\:{the}\:{wide}\:{of} \\ $$$${the}\:{rectangle}\:{is}\:{twice}\:{width}\:{a}\:{of}\:{the}\:{square} \\ $$$${what}\:{is}\:{the}\:{surface}\:{of}\:{the}\:{grey}\:{area}…

lim-x-y-0-0-x-3-2-y-x-3-y-2-

Question Number 114790 by manuel2456 last updated on 21/Sep/20 $$\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\:\frac{{x}^{\mathrm{3}/\mathrm{2}} {y}}{{x}^{\mathrm{3}} +{y}^{\mathrm{2}} }=? \\ $$ Answered by Olaf last updated on 26/Sep/20 $${f}\left({x},{y}\right)\:=\:\frac{{x}^{\mathrm{3}/\mathrm{2}} {y}}{{x}^{\mathrm{3}}…

Question-114784

Question Number 114784 by Khalmohmmad last updated on 21/Sep/20 Answered by PRITHWISH SEN 2 last updated on 21/Sep/20 $$\:\frac{\left(\mathrm{x}−\mathrm{y}−\mathrm{2}\right)\left(\mathrm{x}+\mathrm{y}−\mathrm{2}\right)}{\left(\mathrm{x}−\mathrm{y}\right)\left(\mathrm{x}+\mathrm{y}−\mathrm{2}\right)}=\:\frac{\left(\mathrm{5}−\mathrm{2}\right)}{\mathrm{5}}=\frac{\mathrm{3}}{\mathrm{5}} \\ $$ Commented by Khalmohmmad last…