Suvrat's New Writeupshttp://everything2.com/?node=New%20Writeups%20Atom%20Feed&foruser=Suvrat2004-03-08T03:38:29ZHaiti (idea)http://m.everything2.com/user/Suvrat/writeups/HaitiSuvrathttp://m.everything2.com/user/Suvrat2004-03-08T03:38:29Z2004-03-08T03:38:29Z<p>
<u>What is happening in Haiti? </u>
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On February 29th, 2004, the democratically elected president of <a href="/title/Haiti">Haiti</a>, <a href="/title/Jean-Bertrand+Aristide">Jean-Bertrand Aristide</a> was removed from power by a right-wing paramilitary force with ties to the US. Flown out of the country on a <a href="/title/US">US</a> chartered plane, Aristide is now in exile in the <a href="/title/Central+African+Republic">Central African Republic</a>.
It appears the civil institutions have crumbled, and the capital city <a href="/title/Port-au-Prince">Port-au-Prince</a> has experienced spasms of violence. More than a thousand American marines and hundreds of French, Canadian and Chilean troops have landed in the capital. American diplomats are trying to install a prime minister of their choice in the country.
Aristide departed in murky circumstances with allegations that he was 'kidnapped' by US marines. The 15 nation <a href="/title/Caribbean+Community">Caribbean Community</a> - CARICOM - has called for a United Nations investigation. On Thursday, March 4th, CARICOM was joined by South Africa. The <a href="/title/Black+Congressional+Caucus">Black Congressional Caucus</a> has also expressed concern at the behavior of the<!-- close unclosed tag --></p>…Gujarat (place)http://m.everything2.com/user/Suvrat/writeups/GujaratSuvrathttp://m.everything2.com/user/Suvrat2002-08-15T17:18:16Z2002-08-15T17:18:16Z<p>
I must write about the communal riots mentioned above.
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Please read my node on the <a href="/title/RSS">RSS</a> for a description of the right-wing fascist organizations active in <a href="/title/India">India</a> today. Collectively, the Rashtriya Swayamsevak Sangh, the Vishwa Hindu Parishad, the Shiva Sena, the Bhartiya Janata Party and other organizations form the Sangh Parivar.
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<p>
As I mention in the RSS node, the major political front of the Sangh Parivar -- the BJP -- is in power at the center today. Unfortunately, for the BJP, their electoral fortunes seem to be sagging and they have lost a number of assembly elections recently (India has a <a href="/title/federal">federal</a> system -- assembly elections are elections in a State).
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The BJP is in power in <a href="/title/Gujarat">Gujarat</a>, but a few months ago, it seemed highly likely that they would lose the next elections. The BJP has consistently been whipping up hysteria -- partly communal and partly by creating tension with <a href="/title/Pakistan">Pakistan</a>. However, this time, the Sangh Parivar obviously felt that some drastic<!-- close unclosed tag --></p>…resistor color code (idea)http://m.everything2.com/user/Suvrat/writeups/resistor+color+codeSuvrathttp://m.everything2.com/user/Suvrat2002-08-02T13:50:12Z2002-08-02T13:50:12Z<p>
Couple of small additions. First, each <a href="/title/colour">colour</a> has a single value. So the numbers in band 3 are not <a href="/title/independence+struggle">independent</a> of the numbers in band 1 or band 2. The third band simply tells you how many zeroes to put in front. So <a href="/title/brown">brown</a> is one, and a brown in the third place, tells you to put one <a href="/title/zero">zero</a> in front of the number obtained using the other two bands.
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So for example if you have Red,Red, Orange -- you would interpret it by writing 22 and following it with 3 zeroes. Thus the final value would be 22,000 <a href="/title/ohm">ohms</a>.
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<p>
Second,the following sentence is often helpful in remembering the <a href="/title/sequence">sequence</a> of <a href="/title/colour">colours</a> involved here.
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<b>
B.B. ROY of Great Britain had a Very Good Wife
</b>
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Of course, we find this only in <a href="/title/India">Indian</a> textbooks, because <a href="/title/Rob+Roy">Roy</a> is a <a href="/title/Bengal">Bengali</a> name. You could always change the surname to something you are more comfortable with!
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Russell's paradox (idea)http://m.everything2.com/user/Suvrat/writeups/Russell%2527s+paradoxSuvrathttp://m.everything2.com/user/Suvrat2002-06-01T13:28:23Z2002-06-01T13:28:23Z<p>The <a href="/title/Barber%2527s+paradox">Barber's paradox</a> is slightly different from Russell's paradox. The <a href="/title/Russell%2527s+paradox">Russell's paradox</a> pointed to a problem in the definition of a set. The <a href="/title/barber%2527s+paradox">barber's paradox</a> has its roots in the fact that the barber is "ill defined".
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<p> This is a <a href="/title/subtle">subtle</a> issue but the fact is that when you say that the "barber shaves all those people who dont shave hemselves" the statement is contradictory. So this is a problem of <a href="/title/semantics">semantics</a> and not equivalent to the Russel's paradox. You have simply not defined the <a href="/title/barber">barber</a> properly.
</p>continuous (idea)http://m.everything2.com/user/Suvrat/writeups/continuousSuvrathttp://m.everything2.com/user/Suvrat2001-06-16T03:33:31Z2001-06-16T03:33:31Z<p>
Probably the simplest way to understand the concept of a <a href="/title/continuous+function">continuous function</a> is to think of <a href="/title/real+function">real functions</a> of a <a href="/title/real+variable">real variable</a>. Something like x<sup><small>2</small></sup>
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Here, the word <a href="/title/continuous">continuous</a> means that the <a href="/title/graph">graph</a> of a <a href="/title/function">function</a> should have no breaks. Note that continuity is not a smoothness property. |x| is a continuos function but it has a wedge at the origin. The <a href="/title/step+function">step function</a> is discontinuous. 1/x is discontinuous at zero, because on one side of zero it goes off to +<a href="/title/infinity">infinity</a> and on the other side it goes of to -<a href="/title/infinity">infinity</a>.
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Now lets consider a function of two variables. Here the function would trace out a <a href="/title/surface">surface</a>. Again, we say that it is continuous if the surface has no breaks in it.
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<p>
All this thing about epsilons and deltas essentially means that if the function has one value at a point, and then if I move slightly away from that point, the value of the function should not change drastically!
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Mean value theorem (idea)http://m.everything2.com/user/Suvrat/writeups/Mean+value+theoremSuvrathttp://m.everything2.com/user/Suvrat2001-06-16T03:19:50Z2001-06-16T03:19:50Z<p>
To be precise the two hypothesis you need for the mean value theorem to hold are:
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1)The <a href="/title/function">function</a> f is <a href="/title/continuous">continuous</a> in the <strong><a href="/title/closed+interval">closed interval</a></strong> a,b
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2)The <a href="/title/function">function</a> f is <a href="/title/differentiable">differentiable</a> in the <strong><a href="/title/open+interval">open interval</a></strong> a,b
</p>
<p>
Here's the proof:
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Let k be (f(b)-f(a))/(b-a)
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Consider the <a href="/title/function">function</a> defined as:
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g(x)=f(x)-kx
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Then it is easy to show that:
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g(a)= (bf(a)-af(b))/(b-a) = g(b)
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By <a href="/title/Rolle%2527s+Theorem">Rolle's Theorem</a> the derivative of g must vanish on the <a href="/title/open+interval">open interval</a> a,b. Thus there must exist a point c such that
<br>
g'(c)=f'(c)-k = 0
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At this point c:
<br>
f'(c)=k
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Thats it. Q.E.D
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