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Questions tagged [intuition]

Mathematical intuition is the instinctive impression regarding mathematical ideas which originate naturally without regard to formal mathematical proofs. It may or may not stem from a cognitive rational process.

To have intuition about a mathematical truth is to have some insight into why it is true, and to understand the motivation for talking about that truth in the first place. This is usually stated in contrast with merely having a superficial knowledge of a mathematical truth as a fact, or only having skills at applying a mathematical truth to solve a problem without having the conceptual understanding of solution.

For a nice explanation of mathematical intuition with examples, and links to other articles on developing mathematical understanding, see Developing Your Intuition For Math on BetterExplained.com.

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Which math discipline should i learn to become familiar with rewriting equations?

In my self study of calculus, I've found that there are examples in the books i read where the author rewrites an equation or expression either as part of a logical step in a proof, or to simplify it so that he can perform other desired operations…
user1299028
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Population average age decreases with births AND deaths (kind of)?

When a baby is born, it's easy to see the average age of the population decreases. Intuitively, therefore, when a person dies, the average age of the population must increase to compensate. However, this isn't always true. If the person who dies is…
user2469
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Intuition for why repeated sum of digits of a number is concurrent modulo 9?

I have come across this question where I have to sum the digits of the number repeatedly until it reduces to single digit, for example 9998 can be reduced to 35 which then it can be reduced to 8. So, 8 is the answer. There is correlation between…
commonSense
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What's the intuition for Cross Multiplication?

I already know, I'm NOT asking about, the algebra. It's NOT intuitive why 3 pears x 4 tangelos = 6 quinces x 2 riberries $\iff$ 3 pears/6 quinces = 2 riberries/4 tangelos. I stumbled the picture below, but how does it proffer intuition?
user53259
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Discrete Mathematics - Unsure where to start when dealing with proof

If anyone could me any advice/direction of how to approach this problem, I'd greatly appreciate it. I couldn't find anything on the internet that looked or was similar to proving this type of proof. The fact that that there are irrational numbers…
Woody
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How this solution is working?

In the question asked here, task is to convert decimal numbers to alphabets, like 1: A 2: B . . . 26: Z 27: AA . . . 703: AAA the method used to generate the alphabets is :: 1: subtract 1 from the number 2: calculate number % 26 where % is…
Eight
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Custom equation guidance

i was having a tough time deciding on which SE site to post this rather unique question being that it would help me with a program I'm writing. I decided to come to you guys, not hoping that you would come up with the equation for me, but rather…
davedno
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Sine as derivative of cosine and vice versa.

The derivative of the sine of angle is the cosine of the same angle. Depending on which book you look at or which teacher you ask or which website you're looking at, I've seen it as derivative of sine is negative cosine, derivative of cosine is…
Bobby Brown
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How can school children intuit why over 100, D is larger? But under 100, D% is larger?

I can prove the Rule of 100 algebraically, below. But my school kids are hankering after intuition, and a plainer explanation. Follow the Rule of 100 Should discounts be percentages or absolutes? Consider a \$150 blender. Should you offer 20%…
user1147844
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