Archimedean Property Of Real Numbers | Imp. Theorem | Proof | Properties of Real Numbers | Bsc.

[@OMGMaths]

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Your teaching style is so simple mam . thank you so much

[@OMGMaths]

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[@Modesta.warnerWarner-sr1xl]

Greetings @@OMGMaths I'm using this Archenedean Axiom to prove that 0.999... = 1 ■■■■■■■■■ Asume that 0.999... < 1 This means that 0 < (1 - 0.999...) < 1 By the Axiom of Archimedes, there exists and natural number, say n, that satisfies the following : n(1 - 0.999...) > 1 Thusly n > [1 \ (1 - 0.999...)] Choosing: n = ROUNDING UP [1 + 1/(1 - 0.999...)] Here I got stuck.

[@angelofelisimolacruz1462]

Ancestor Modesta Warner wrote: Greetings @OMGMaths I'm using this Archenedean Axiom to prove that 0.999... = 1 ■■■■■■■■■ Asume that 0.999... < 1 This means that 0 < (1 - 0.999...) < 1 By the Axiom of Archimedes, there exists and natural number, say n, that satisfies the following : n(1 - 0.999...) > 1 Thusly n > [1 \ (1 - 0.999...)] Choosing: n = ROUNDING UP [1 + 1/(1 - 0.999...)] Here I got stuck.

[@angelofelisimolacruz1462]

For any natural number p < n it follows that p(1 - 0.999...) < 1 Let M be the set {p ∈ ℕ | p(1 - 0.999...) < 1} ⊆ ℕ It follows that |M| < n = least upper bound of (M) Conjecture: M {p ∈ ℕ | p(1 - 0.999...) < 1} = ℕ which is a contradiction. Hense the assumption 0.999... < 1 is false. Therefore 0.999... must be equal to 1.

[@suganthit7172]

Your class is so nice. Please send videos of total real analysis

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[@khabdullah2694]

Very good explanation mam..thank u a lot...❤❤

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Start again, you teach very well.👌

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Yes mam

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Owsemm teaching style

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Thank you for the explanation!

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[@asimwrites1633]

Really appreciable ma'am... U have a nice skills of teaching... May God bless u 🥰 But mam i think that u-1 should be least upper bound of A and not just upper bound.

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Mam make more video your teaching style to good.

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[@tuba4588]

maam bht confusion horhi hai please help...ye archimedean property DU ki readings m to alg hai " if x € R , then there exists a natural number n0 such that x

[@tanuseth784]

Very nice explanation thanku you so much mam...

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Thank you so much mam very helpful video 😇😇

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Awesome video

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Ma'am well ordering principal par video bana dijiye

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Wow ma'am amazing explanation 😚😚🙏

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Tq so much mam😘❤ plz algebra bhi krba do Maine Maine topic humble request your teaching way is so expensive

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@@OMGMaths assalam o Alikum mam

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Thnku mamm.. But last ma for some values of N aayga yaah for all?

[@TanujMeena-zs9ji]

didi, can you also teach us mathematical induction or rational number

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I like it. Nice demo

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👍 great

[@chiheero]

Mam archimedian property real analysis m bhi yhi hai ya different h ?I mean Jo aapne yha explain Kia h yeh real numbers ko consider Krke kia h toh kya dono , for real analysis similar hee h ?

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Yes mam

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teacher ! Why did you stop making videos?

[@inmathsstar]

Mam kindly make video on density theorem And Monotone sequence,balzano weierstrass theorem and in k theorems Mujy aur kisi ki smajh ni ati Please 🥺

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Reals ki kon si book achi hai

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1 number madam ji

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Thanks mam

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Tysm

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August me Mera exam hai?

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❤lv u mam..

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