Kwa Wataalam wa hesabu

Je unajua kuwa 2 = 1?

Wataalam wa hesabu tunasema kuwa kama x=y
basi 2x=2y
kwahiyo 2x-x = 2y-y si sawa?
Maana yake ni kuwa 2x-2y = x-y hapo hakuna ubishi naamini.
Hii ni sawa na kusema 2(x-y) = (x-y)
kwamba 2(x-y)/(x-y) = (x-y)/(x-y)
Na hiyo inathibitisha kuwa 2 = 1
Kwa wasiojua hesabu watabaki wanatoa mimacho, hawaelewi kitu halafu bahati mbaya watabisha!

Good Day Mathematicians!

Chrispin said:

Je unajua kuwa 2 = 1?

Wataalam wa hesabu tunasema kuwa kama x=y
basi 2x=2y
kwahiyo 2x-x = 2y-y si sawa?
Maana yake ni kuwa 2x-2y = x-y hapo hakuna ubishi naamini.
Hii ni sawa na kusema 2(x-y) = (x-y)
kwamba 2(x-y)/(x-y) = (x-y)/(x-y)
Na hiyo inathibitisha kuwa 2 = 1
Kwa wasiojua hesabu watabaki wanatoa mimacho, hawaelewi kitu halafu bahati mbaya watabisha!

Good Day Mathematicians!

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Wengine tuliacha kusoma HESABU darasa la nne na kuanza kusoma HISABATI. Kwa hiyo kukubishia ni rahisi tu!!!!

The Farmer said:

Wengine tuliacha kusoma HESABU darasa la nne na kuanza kusoma HISABATI. Kwa hiyo kukubishia ni rahisi tu!!!!

Click to expand...

Mkuu kuna tofauti gani kati ya hesabu na hisabati?

Chrispin said:

Je unajua kuwa 2 = 1?

Wataalam wa hesabu tunasema kuwa kama x=y
basi 2x=2y
kwahiyo 2x-x = 2y-y si sawa?
Maana yake ni kuwa 2x-2y = x-y hapo hakuna ubishi naamini.
Hii ni sawa na kusema 2(x-y) = (x-y)
kwamba 2(x-y)/(x-y) = (x-y)/(x-y)
Na hiyo inathibitisha kuwa 2 = 1
Kwa wasiojua hesabu watabaki wanatoa mimacho, hawaelewi kitu halafu bahati mbaya watabisha!

Good Day Mathematicians!

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So what are you trying to say?

mkuu nikiwa bored siku zote ndio huingia huku kwa jokes ku relax sasa leo duhh najuta kuingia huku

Chrispin said:

Mkuu kuna tofauti gani kati ya hesabu na hisabati?

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Hesabu ni (Kujumlisha, kuzidisha etc),

Chrispin said:

Je unajua kuwa 2 = 1?

Wataalam wa hesabu tunasema kuwa kama x=y
basi 2x=2y
kwahiyo 2x-x = 2y-y si sawa?
Maana yake ni kuwa 2x-2y = x-y hapo hakuna ubishi naamini.
Hii ni sawa na kusema 2(x-y) = (x-y)
kwamba 2(x-y)/(x-y) = (x-y)/(x-y)
Na hiyo inathibitisha kuwa 2 = 1
Kwa wasiojua hesabu watabaki wanatoa mimacho, hawaelewi kitu halafu bahati mbaya watabisha!

Good Day Mathematicians!

Click to expand...

si kweli, hesabu huwa haziendi hivyo kama utakavyo wewe bali zina principal zake
kama x=y,
ukija hapa, 2x=2y, kwa nini umetumia mbili, vipi ikiwa tatu yaani 3x=3y
kwa hiyo 3x-x=3y-y
maana yake ni kuwa 3x-3y=x-y
hii ni sawa na kusema 3(x-y)=(x-y)
kwamba 3(x-y)/(x-y)=(x-y)/(x-y)
na hiyo inathibisha kuwa 3=1
HAYA WEWE UNAEJUA HESABU KANUSHA BAC

Kituko said:

si kweli, hesabu huwa haziendi hivyo kama utakavyo wewe bali zina principal zake
kama x=y,
ukija hapa, 2x=2y, kwa nini umetumia mbili, vipi ikiwa tatu yaani 3x=3y
kwa hiyo 3x-x=3y-y
maana yake ni kuwa 3x-3y=x-y
hii ni sawa na kusema 3(x-y)=(x-y)
kwamba 3(x-y)/(x-y)=(x-y)/(x-y)
na hiyo inathibisha kuwa 3=1
HAYA WEWE UNAEJUA HESABU KANUSHA BAC

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Mkuu nakukaribisha kwenye chama chetu cha WANAUJUA HESABU!

kwa mantiki hiyo any number can be proved equal to one with the exceptional of zero!

Chrispin said:

Je unajua kuwa 2 = 1?

Wataalam wa hesabu tunasema kuwa kama x=y
basi 2x=2y
kwahiyo 2x-x = 2y-y si sawa?
Maana yake ni kuwa 2x-2y = x-y hapo hakuna ubishi naamini.
Hii ni sawa na kusema 2(x-y) = (x-y)
kwamba 2(x-y)/(x-y) = (x-y)/(x-y)
Na hiyo inathibitisha kuwa 2 = 1
Kwa wasiojua hesabu watabaki wanatoa mimacho, hawaelewi kitu halafu bahati mbaya watabisha!

Good Day Mathematicians!

Click to expand...

Hahahahahahahahahaa
Ni swali ambalo unaweza ukamuuliza mwanafunzi, wapi pana kosa! Ninaamini wewe unajuwa kosa lipo wapi. Kama unafahamu kuwa zero divide by zero can be certain number, depending to the nature of the numerator and denominator....kama ni zero gawanya kwa zero basi tunaweza kutumia L'Hospitals rule.
Kwanini nasema zero gawia zero? Ulipofika x-y/x-y; hi ni sawa na 0/0 maana x=y. Sasa ikiwa hiyo Never conclude kwamba ni 1.
Ninaamini nimeeleweka wapi palipo kufanya u-conclude kuwa jibu ni moja. Jiulize kwanini namba yoyote ukiigawa yenyewe kwa yenyewe jibu ni moja lakini 0 gawa kwa 0 si moja?

Baba Mkubwa said:

Hahahahahahahahahaa
Ni swali ambalo unaweza ukamuuliza mwanafunzi, wapi pana kosa! Ninaamini wewe unajuwa kosa lipo wapi. Kama unafahamu kuwa zero divide by zero can be certain number, depending to the nature of the numerator and denominator....kama ni zero gawanya kwa zero basi tunaweza kutumia L'Hospitals rule.
Kwanini nasema zero gawia zero? Ulipofika x-y/x-y; hi ni sawa na 0/0 maana x=y. Sasa ikiwa hiyo Never conclude kwamba ni 1.
Ninaamini nimeeleweka wapi palipo kufanya u-conclude kuwa jibu ni moja. Jiulize kwanini namba yoyote ukiigawa yenyewe kwa yenyewe jibu ni moja lakini 0 gawa kwa 0 si moja?

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L'Hospital's Rule ina matumizi yake sehemu fulani....nimeiweka hapa kama mfano, may be can't work. Nakumbuka nimeitumia L'Hospital's Rule nilipokuwa natafuta limits, na naitumia kukiwepo cases furani mfano ikatokea 0 gawa 0!!!!

you got it all wrong!
First, number of angles in 2 can never be equal to number of angles in 1, which is the basis for having numbers.
Secondly, look if x=y then 2x=2y, that is correct, now
2x-x=2y-y also correct, but down here is where you went wrong
2x-2y =x-y ( this is incorrect) but rather 2x-2y=-y+x. Note that -x+y is not the same as y-x bse subtraction is not commutative , i.e 2-3 not same as 3-2 !

Matarese said:

you got it all wrong!
First, number of angles in 2 can never be equal to number of angles in 1, which is the basis for having numbers.
Secondly, look if x=y then 2x=2y, that is correct, now
2x-x=2y-y also correct, but down here is where you went wrong
2x-2y =x-y ( this is incorrect) but rather 2x-2y=-y+x. Note that -x+y is not the same as y-x bse subtraction is not commutative , i.e 2-3 not same as 3-2 !

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May be I am wrong mkuu!
It is true that subtraction is not commutative. If 2x-x = 2y-y then it is true that 2x-2y=x-y....this is simple maths kwasababu we have added -2y to the equation 2x-x=2y-y, tukapata 2x-2y-x=-y and then tukajulisha tena x, tukapata 2x-2y=x-y. Commutativity imetumika kwenye cases kama -2y+2x=2x-2y (bado tupo kwenye addition). Ni kweli 2-3 si sawa na 3-2 lakini 2-3 ni sawa na -3+2. Kwahiyo, if 2x-x=2y-y then 2x-2y=x-y (tutatumia commutativity).....nahisi nipo sahihi.

Tukirudi kwenye issue ya thread kwamba 2=1; mimi nimeona kosa lipo kwenye x-y/x-y......yaani 0/0 siyo moja!!!....nahisi nipo sahihi

Nawasilisha

Baba Mkubwa said:

... Kama unafahamu kuwa zero divide by zero can be certain number, depending to the nature of the numerator and denominator....kama ni zero gawanya kwa zero basi tunaweza kutumia L'Hospitals rule.
Kwanini nasema zero gawia zero? Ulipofika x-y/x-y; hi ni sawa na 0/0 maana x=y. Sasa ikiwa hiyo Never conclude kwamba ni 1.
Ninaamini nimeeleweka wapi palipo kufanya u-conclude kuwa jibu ni moja. Jiulize kwanini namba yoyote ukiigawa yenyewe kwa yenyewe jibu ni moja lakini 0 gawa kwa 0 si moja?

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Baba Mkubwa,

Zero divide by zero sidhani kama inawezi kuwa "a certain number depending on the nature of the numerator and denominator" hata siku moja. Hiyo "depending on" inakuja vipi tena wakati ushafahamu numerator ni zero na denomionator ni zero? Kitu chochote gawanya kwa zero ni undefined, au infinity, period. Haijalishi juu ya zero kuna nini. Alipofika x-y / x-y ilibidi apate undefined, mwisho. Hakuna cha L'Hospitals rule hapa, sidhani.

Buricheka said:

Baba Mkubwa,

Zero divide by zero sidhani kama inawezi kuwa "a certain number depending on the nature of the numerator and denominator" hata siku moja. Hiyo "depending on" inakuja vipi tena wakati ushafahamu numerator ni zero na denomionator ni zero? Kitu chochote gawanya kwa zero ni undefined, au infinity, period. Haijalishi juu ya zero kuna nini. Alipofika x-y / x-y ilibidi apate undefined, mwisho. Hakuna cha L'Hospitals rule hapa, sidhani.

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Nikweli mkuu ulichosema. Ndiyo maana nilipopost kuhusu/kutaja L'Hospital's Rule nikaandika post nyingine ni wapi L'Hospital's Rule inatumika mkuu (inawezekana nimechanganya....which is possible in maths life). Nikasema hutumika wakati fulani, mfano limits.....kwa lugha nyingine kwenye case yake ya zero gawanya kwa zero hatutaweza kutumia L'Hospital's Rule. jibu langu la kusema hutegemeana na numerator and denominator nipo sahihi, nahisi, hasa pale tunapozungumzia limits. Unapoevaluate limits na ukawa na 0/0; Utapata jibu kulinganya na nature ya numerator na denominator NA si moja kila siku.

Baba Mkubwa said:

... na ukawa na 0/0; Utapata jibu kulinganya na nature ya numerator na denominator NA si moja kila siku.

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Brother, hapo ndo nashindwa kukuelewa.

Tunajua kabisa tuna dili na sifuri gawanya kwa sifuri, numerator na denominator zote zinajulikana, sasa utasemaje tena "kulingana na nature ya numerator na denominator"? Nature si ushaijua kaka? Ambayo ni sifuri juu, sifuri chini, sivyo?

Buricheka said:

Brother, hapo ndo nashindwa kukuelewa.

Tunajua kabisa tuna dili na sifuri gawanya kwa sifuri, numerator na denominator zote zinajulikana, sasa utasemaje tena "kulingana na nature ya numerator na denominator"? Nature si ushaijua kaka? Ambayo ni sifuri juu, sifuri chini, sivyo?

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Okay nimekupata wapi ambapo sijaeleweka, inawezekana maelezo yangu si timilifu....
L'Hospital's Rule nimeizungumza itakapotumika kwenye limits. 0 gawa kwa 0 huweza kupatikana pale utakapo weka x goes to certain number. Naomba nitoe mifano:

1. limit of sinx/x as x goes to 0 jibu ni 1. Tulipo-evaluate limit tulipata 0/0 ndipo tulipotumia L'Hospital's Rule na tukapata jibu 1

2. limit of (cosx-1)/x as x goes to 0 jibu ni 0. Tulipo-evaluate limit tulipata 0/0 ndipo tulipotumia L'Hospital's Rule na kupata jibu 0

3. limit of sin(2x)/x as x goes to 0 jibu ni 2. Tulipo-evaluate limit tulipata 0/0 ndipo tulipotumia L'Hospital's Rule na tukapata jibu 2

etc
Kwahiyo navyosema jibu hutegemeana na nature ya numerator and denominator namanisha kuwa jibu litategemea swali lipoje. Inawezekana maelezo yangu si timilivu mkuu. Inawezekana sijajuwa matumizi ya "nature" na "depends on"...lugha kaka/dada

Nawasilisha

Before you try to calculate you have to understand this:
1. You are trying to verify two values that have completely different angles. Which is immaterial.
2. When you try to divide 2(x-y)=(x-y) the answer is always undefined because the form 0/0 is indeterminate form, whose division is immaterial (undefined) as above unless L'hospitals rule is applied. There are so many such forms. Thus the above ( i am not sure if the person is trying to prove, or verify or show) is quite untrue.

Matarese said:

Before you try to calculate you have to understand this:
1. You are trying to verify two values that have completely different angles. Which is immaterial.
2. When you try to divide 2(x-y)=(x-y) the answer is always undefined because the form 0/0 is indeterminate form, whose division is immaterial (undefined) as above unless L'hospitals rule is applied. There are so many such forms. Thus the above ( i am not sure if the person is trying to prove, or verify or show) is quite untrue.

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Nikweli mkuu ulichosema ingawa muanzalishi wa thread alitoa changamoto ambayo inamuwezesha mtu kujuwa wapi pana kosa. 2=1 is true to some places of algebra (with addition of more information eg modulus):::: are you talking about........linear algebra, abstract algebra, descrete algebra/boolean algebra etc.

Sijui hesabu na hivyo siwezi kuchangia lakini nimefurahi kuona kwamba kuna watu wanajua hesabu humu JF.

Cheers,

Tiba