Recent content by LittleRookie

I totally agree, this is how I view Mathematics now (but not so in the past), which leads to a few questions in this thread that I've recently posted. https://www.physicsforums.com/threads/before-understanding-theorems-in-elementary-euclidean-plane-geometry.982441/ Unfortunately, I haven't...

We can also say we want to have a number x that is less than 1/n for any positive integer n. Then, people in the past would have come up with a different standard list of axioms for real numbers (because the current one contradicts this idea). However, we do not want to have x in our real number...

Before looking at the proof of basic theorems in Euclidean plane geometry, I feel that I should draw pictures or use other physical objects to have some idea why the theorem must be true. After all, I should not just plainly play the "game of logic". And, it is from such observations in real...

😮 Why so? Please enlighten me. 🙏

I meant if the author discusses a theorem and its proof, then the least that the author can do is to provide a complete proof, or if the proof requires further knowledge, the author can mention which cases are not provided with proof because so and so. Furthermore, the complete proof of the...

Every explanation about scaling a 2D vector, or equivalently having a line segment PQ on cartesian plane and then find a point R on the line PQ satisfying PR/PQ = r (fixed given r) starts with that one specific case in the picture. A formula for the coordinates of R is then given for that case...

I read the page in the past, but I didn't get much out of it. Can you help me with my questions instead? I really want to know!

Hello, I have a few questions about mathematics as a deductive system in which mathematical statements follow as a logical consequence from axioms and other statements. In particular, consider the real number system and Euclidean geometry. Is doing arithmetic with numbers and working on...

If the scientist obtain a number from experiment that is different from the calculated number according to some Scientific law, is the Scientific law disproved? I need help on these questions. I'm very curious in knowing how does Scientist test the accuracy of a Scientific law/theory. I see...

I don't really understand. Can you explain in simpler terms? Like I'm five.

1. No matter how many reindeer we have checked, we can't prove that reindeer can't fly. 2. I guess a couple of reindeer? But I will think that reindeer can't fly based on current findings, but perhaps there is one that flies and we don't know of it. 3. One

How is a Scientific law or theory's accuracy tested? I've searched online about verification of Newton's law but the materials are unhelpful. Many show an experiment that verifies a particular instance of the law and then concludes the law is verified. We all know that there are infinite...

I understand that. I'm seeking help in the interpretation of multiplication of irrational numbers in the real world. Something similar to the real world interpretation of multiplication of rational numbers, for instance, 1/2 times of 3 can be interpreted as divide 3 into 2 parts, and take 1 out...

I need more help :(

I'm aware of the axioms of real numbers, the constructions of real number using the rational numbers (Cauchy sequence and Dedekind cut). But I can't relate the arithmetic of irrational numbers to real world usage. I can think the negative and positive irrational numbers to represent...