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Let's start with a question, "Can I be in a different position at the same time ?" Obviously - No. Ok, let's ask the question more specifically, "Can I be in a mood of happy and sad at the same time ?" 🤔🤔🤔 Well, we can say many times in life we are not actually happy or sad, if we try to measure on a scale starting 1 with sadness and 10 with happiness, we may be in between 1 and 10. Let at 1 sad, 2 - 4 is more likely sad, 5,6 neither happy nor sad, 7 - 9 is more likely happy and at 10 is happy. Have a look at the following table and graph - (Scores actually represent inner psychological feelings) So for the whole day, since the average of all scores is 7, we can say more likely happy is the experimented mood, but if we see the data locally it does not say so, it can say we are in some ups and down combination of happy and sad (like a wave spread in a whole day). Two clever observations I would like to mention here, 1. As I mentioned earlier, although

The development of Linear Algebra

Linear Algebra is the most useful and powerful tool in Mathematics. In the last blog " Linear Algebra - Purpose to Application " we saw how a higher-order system of linear equations has been solved by transforming the equation into the matrix. Although it's good to mention that it only works if in the AX=B [A is m*n, X is n*1, B is m*1, so it has m equations and n unknowns ] our A matrix is invertible, if it is not invertible i.e, in the sense of matrix it is rank of A is less than n and rank of (A;B) = rank of A < n, so the system of linear equation AX=B has infinitely many solutions, we can find the solution by converting the A matrix into row-echelon form, simply you will get the solution from bottom. Note:- 1. The rank of a matrix - It is defined as the largest order square matrix whose determinant is non-zero. 2. Row-echelon form - We said a matrix is in a row echelon form if in the matrix fo

The Axioms - Probability

The word " Probability " often comes into our day-to-day life referring to, " What is the probability of some random event ? " simply saying what at most chance the event to occur. In my last blog " What is the probability you will open this blog ? " I told you, why for a long time, I have been in a dilemma, about why probability is so useful , my counter-argument was, "Probability tells us about the most probable event to happen based on the available ones, it does not give us the guarantee that the event to be happened for sure, then why it's so overrated ?" and I give you a classical definition of probability. Although the classical definition easily gives us the probability, it has some ambiguity . 😢😢 1) It is applicable when the total number of events are finite. 2) All the events in the event space should be equally likely (they should be symmetrical with eac

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TANMAY SAHA: I am passionate about mathematics.As a mathematician every new thing that we saw in our usual routine thats challenge my mathematical knowledge and gave me a chance to find is it logical or something illogical happened surround us which is really amazing in itself, make me passionate about my field of study give me challenge to solve it .I always try to find new things in mathematics that help me explain and think in different way or make existing ways more powerful. I really loved it to do mathematics.

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