0.999... = 1

Today I was reading some forum where engineers and mathematicians fighting over an equation

0.999... = 1


Engineers say that is wrong.0.999... is only approximately equal to 1. Mathematicians say it is exactly equal to 1.
Before I judge who is correct let me see whether I am an engineer or a mathematician.Hmmm. Tough question ?Not really, I can easily decide on mathematicians side because I definately know that I am not an engineer.Though my degree says I am an Aerospace Engineer ,I haven't learnt or remembered about anything which I learnt regarding engineering or aerospace.Even if you disagree I am gonna settle with mathematics.

Coming to the equation, Eng's argument is that we cannot really approximate and say it is equal and they argue that by saying 0.999...=1 we are rounding off.Mathematicians argue that 0.999... with 3 dots at the end implies that the 9 is a repeating decimal infinitely.So it is equal to 1.

Actually, we can prove this.

lets say x=0.999....
10x = 9.999...
---------
10x - x = 9.000....
that means 9x = 9 => x=1
Hence proved :)

There are other solutions also but I like this one.

Who contributed more for Indian Test wins in this millennium? : Batting in Indian Home wins

So last time I looked at away wins here and now I ll take up Indian wins.Before I look at the stats let me make some guesses.One thing for sure,like in a way wins Dravid and Sachin should be the most contributors.Sehwag should have made more contribution compared to his contribution in away wins.I also expect Sachin to be more contributing than Dravid.Lets see the stats.

Player	Span	Mat	Inns	NO	Runs	HS	Ave	BF	SR	100	50	0	4s	6s
SR Tendulkar	2000-2010	24	40	6	2226	214	65.47	4118	54.05	8	10	0	276	12
R Dravid	2000-2010	23	39	9	2168	200*	72.26	4583	47.30	7	9	1	261	5
V Sehwag	2002-2010	18	30	1	1810	293	62.41	2020	89.60	4	11	1	253	32
VVS Laxman	2000-2010	22	32	5	1533	281	56.77	2839	53.99	3	11	1	208	1
SC Ganguly	2000-2008	15	25	2	947	136	41.17	1885	50.23	2	3	2	119	7
MS Dhoni	2005-2010	14	19	4	928	132*	61.86	1423	65.21	2	8	0	85	18
G Gambhir	2004-2010	11	19	0	672	167	35.36	1146	58.63	2	3	1	75	1

In the overall runs Sachin and Dravid pretty close.However, Dravid beats Sachin by his average. Sehwag is also not far considering he played less innnings. If you take average runs scored per innings I think Sehwag(60.33) beats both Sachin(55.65) as well as Dravid(55.59).Even Dhoni's average is good in these matches which means he is actually contributing to Test cricket also.I am surprised.But Gambhir failed at home clearly.He was really good in away wins but didn't really contributed much here.
So Its the trio of Dravid,Sachin and Sehwag are the batsmen who contributed mostly for Indian home wins.
I would give the trophy to Sehwag here because he scored at 60 per innnings at the strike rate of 90.
Silver and bronze goes to Dravid and Sachin non-respectively.Laxman and Dhoni chipped in at times but Ganguly and Gambhir failed at home wins.

India in South Africa: If I can dream

So SA declared early to counter the rain gods. India started their innings trailed by 430 and were really fighting it out there. Thanks to Sehwag and Gambhir we are now 294 behind only.

As a raional cricket fan I should only be looking at saving the match if not loosing it rightaway.But then I am an Indian fan and I would still think the Indian win is possible. After alll India is the world No 1.Lets think about a possibility.

4th day 1st session: Ishant will play his natural play and provide good support to Rahul and will make a partnership of 40 in the first hour. At this time Sachin enters shows hist stroke play and Rahul also picks up and will make a partner ship of 100 in next 1 n half hr. Ya its an early start so 2 and half hr session it is.So would be 330/3

2nd session: Rahul and Sachin continues and Rahul completes his Century and also Sachin his 50th. Both will not give wickets to safaris and will milk 120 from that session.India would be 450/3 with 20 run lead.Remember I am dreaming.

3rd session: Sachin falls here with the special entrance by Laxman with 3 4's in a row.So my favorite partnership continues and will milk another 120 in the session with India at 570/4. We will be leading by 140 then.Rahul will be at 180 and Laxman completes his yet another half century.

5th Day 1st Session: Rahul will complete his double and trying to shift gears ll loose his wicket with Raina coming. Laxman will not make his century and Dhoni comes onto the crease. In the next 1 and half hr Raina and Dhoni blasts SA bowlers and milk 150. India declared with 5 overs still to play in that session.SA will have a target of 291 and will make fascinating two sessions left to ponder about.

Next two sessions : I don't want to dream them I want to see them live :D

Who contributed more for Indian Test wins in this millennium?

I was just wondering who are the players who contributed for India in attaining the numero 1. So thought of analyzing the same.

Lets start with batsmen.For the record I am only taking the matches in this millennium as I think India started winning test matches consistently from 2000. That was the time of Sehwag coming into the side and Dravid, Laxman and Ganguly being in their best form.That was the time when India started depending on a team performance rather than master balster's performance.

Can you guess who would have made the most contribution in the away win matches? For me it was always Dravid, Sehwag, Sachin and to little extent Laxman. I thought its more of Sehwag's runs that made in a hurry ensured the wins.

So here I took a stat from cricinfo.Below are the stats from 1st Jan 2000 to present day where India won away from home. I have taken only the batsmen who have at least scored 500 runs.

View overall figures
Primary team India
Home or away away (home of opposition)
Start of match date between 1 jan 2000 and 18 Dec 2010
Tournament type 2 team series
Match result won match
Qualifications runs scored greater than or equal to 500
Ordered by runs scored (descending)

Overall figures

Player	Span	Mat	Inns	NO	Runs	HS	Ave	BF	SR	100	50	0	4s	6s
R Dravid	2000-2010	22	34	5	2114	270	72.89	4113	51.39	6	9	1	289	4
SR Tendulkar	2000-2010	18	27	5	1866	248*	84.81	3237	57.64	8	4	1	224	7
VVS Laxman	2001-2010	18	27	3	1296	148	54.00	2421	53.53	3	8	0	171	1
V Sehwag	2002-2010	16	25	3	1186	309	53.90	1426	83.16	3	3	3	167	13
SC Ganguly	2000-2008	16	23	4	997	128	52.47	1917	52.00	2	8	2	116	5
G Gambhir	2004-2010	8	13	3	757	139	75.70	1090	69.44	2	5	0	105	1

I was correct on Rahul Dravid as the above stats prove that he is the one who contributed the most for away wins. The one which surprised me most is the Sachin's average here. He has the best average for away wins but when I try to recollect the historic wins I see Dravid, Sehwag and Laxman but I am not able to recollect the matches which are won by Sachin. This shows that Sachin contributed consistently as well as Dravid but others have only clicked in few matches and failed in few matches. So here I can easily say that bulk of the Indian wins away are contributed by Dravid and Sachin.

These stats also tell us that Sehwag is not really contributed that much which contradicts my thinking. I always thought that Sehwag is the one who is doing exceptionally well in tests.He has very less average compared to Sachin,Dravid and laxman.But the real difference here is the strike rate I guess. With a strike rate of 84 if you can average 54 then it becomes very difficult for opposition and it gives a very good platform for the middle order batsmen.

And also once Gambhir is added into this fab 5 it has been raining runs for India. Gambhir averages 76 with a very good strike rate of 70 in away wins only next to Sachin.

One more thing this stat proves that Ganguly was not that bad as was thought by me earlier.All the while I thought Ganguly was in the team only for his captaincy but clearly with an average 53 I think you can pick him in any batting line up as a pure batsmen.

So conclusion, Dravid and Sachin are the most contributors with Sehwag and Gambhir setting up the platform and Ganguly and Laxman chipped in. Its a clear Team effort I say.

In my next analysis I ll take up Home wins. Any guesses who would be the most contributors?

India in South Africa

Before India,the rock stars of cricket world, came to South Africa India is world No.1 in tests as per ICC ranking but everybody has doubts of Indian domination in away matches. Frankly speaking, though India is numero 1 by big margin in ranking, it is still the underdog in the current series.Even if India draws one of the 2 test matches in this series it can still hang on to 1st place.

Though Batting line up is superb for India, the weak link is definitely bowling.With Zaheer being injured, its a no match for likes of Kallis and Amlas.Last time when India toured SA Sreesanth was pick of the bowlers. The way he moved the ball in the first test was amazing. I think SA was folded out for 76 at that time.Never mind, we lost the next two matches to hand over the series to safaris.

So coming to the first test match, India has already folded out for 136 and safaris have already got a lead of 230.As Arun Lal would say, there is no coming back from this hole.It seems most likely that India would be behind by at least 400 by the time they start their second innings with 2 days to play.Still as an India fan, I hope they can save the match like gambhir did in NZ or another Dravid-Laxman partnership.

Though India batting flopped it is still ok they can turn around the form in no time,where as, Indian seamers not being able to take a single wicket on a seaming wicket is unacceptable. I hope sreesanth bowls like he bowled last time in SA and Ishant comes back in form like he did with NZ.Lets see what happens on 3rd day.