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Question Number 7442 by lakshaysethi last updated on 29/Aug/16

is 0×0 not defined or equal to 0? if it is not defined then why?

$${is}\:\mathrm{0}×\mathrm{0}\:{not}\:{defined}\:{or}\:{equal}\:{to}\:\mathrm{0}? \\ $$$${if}\:{it}\:{is}\:{not}\:{defined}\:{then}\:{why}? \\ $$

Commented by Rasheed Soomro last updated on 29/Aug/16

0×0 is defined and it is equal to 0.

$$\mathrm{0}×\mathrm{0}\:{is}\:{defined}\:{and}\:{it}\:{is}\:{equal}\:{to}\:\mathrm{0}. \\ $$

Commented by FilupSmith last updated on 31/Aug/16

x=0 x×x=x^2 =0^2 ∀n∈Z/{0}, x^n =x=0^n =0

$${x}=\mathrm{0} \\ $$$${x}×{x}={x}^{\mathrm{2}} =\mathrm{0}^{\mathrm{2}} \\ $$$$\forall{n}\in\mathbb{Z}/\left\{\mathrm{0}\right\},\:\:\:{x}^{{n}} ={x}=\mathrm{0}^{{n}} =\mathrm{0} \\ $$

Commented by FilupSmith last updated on 31/Aug/16

5×4 is essentually 5 baskets, each basket has 4 apples. Total = 4+4+4+4+4=4×5 0×0 is zero baskets with zero apples each. that is 0+0 (kind of. its more like 0 added to itself zero times, but you cant write that)

$$\mathrm{5}×\mathrm{4}\:\mathrm{is}\:\mathrm{essentually}\:\mathrm{5}\:\mathrm{baskets},\:{each}\:\mathrm{basket} \\ $$$$\mathrm{has}\:\mathrm{4}\:\mathrm{apples}.\:\mathrm{Total}\:=\:\mathrm{4}+\mathrm{4}+\mathrm{4}+\mathrm{4}+\mathrm{4}=\mathrm{4}×\mathrm{5} \\ $$$$ \\ $$$$\mathrm{0}×\mathrm{0}\:\mathrm{is}\:\mathrm{zero}\:\mathrm{baskets}\:\mathrm{with}\:\mathrm{zero}\:\mathrm{apples}\:\mathrm{each}. \\ $$$$\mathrm{that}\:\mathrm{is}\:\mathrm{0}+\mathrm{0}\:\left(\mathrm{kind}\:\mathrm{of}.\:\mathrm{its}\:\mathrm{more}\:\mathrm{like}\:\mathrm{0}\:\mathrm{added}\right. \\ $$$$\left.\mathrm{to}\:\mathrm{itself}\:\mathrm{zero}\:\mathrm{times},\:\mathrm{but}\:\mathrm{you}\:\mathrm{cant}\:\mathrm{write}\:\mathrm{that}\right) \\ $$

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