3 is everywhere - Numberphile

TL;DR

Most integers contain the digit 3, with the proportion increasing as numbers get larger.

Transcript

DR JAMES GRIME: So today, I want to tell you that almost all integers contain the digit 3. So the integers are the whole numbers. So I'm saying that almost all whole numbers contain the digit 3. It sounds strange, doesn't it? Yeah, because I can think of infinitely many numbers that contain a 3. I've got 3, 33, 333, 3,333, and so on. I can think of... Read More

Key Insights

• #️⃣ The percentage of numbers containing the digit 3 increases as numbers grow larger.
• #️⃣ Dr. Grime demonstrates a formula to find the next number containing the digit 3.
• #️⃣ An explanation is given on how the proportion of numbers containing the digit 3 approaches 100% as numbers expand.
• #️⃣ The concept of 'almost all' in mathematics is clarified, highlighting that the proportion nears 100% as numbers increase.
• #️⃣ Dr. Grime mentions that the same principle applies to the digit 5, demonstrating that almost all numbers contain a 5 as well.
• 🙂 The systematic explanation provided by Dr. Grime sheds light on the prevalence of the digit 3 in integers.
• #️⃣ Understanding the relationship between numbers and the presence of the digit 3 is key to comprehending how almost all integers contain this digit.

Questions & Answers

Q: How does Dr. James Grime demonstrate that almost all integers contain the digit 3?

Dr. Grime shows that as numbers increase in size, the proportion of integers containing the digit 3 also increases, approaching 100% as numbers become larger.

Q: What formula does Dr. Grime provide to calculate the next number containing the digit 3?

Dr. Grime offers a formula where you take the last number, multiply it by 9, and add 10 to the power of n to find the next number containing a digit 3.

Q: What is the significance of the proportion getting closer to 1 as numbers become larger?

As numbers increase in size, the proportion approaching 100% implies that almost all integers will contain the digit 3 as the number of digits increases.

Summary & Key Takeaways

• Dr. James Grime explains that almost all integers contain the digit 3 through a systematic explanation.

• The proportion of numbers containing the digit 3 increases as numbers become larger.

• A formula is provided to calculate the number of integers containing the digit 3.