Numbers and Numerals: A Weekend Exploration - Part 2. Sunday

Updated: Aug 12

By Rashmi Jejurikar


Rhea was helping her brother water the garden plants when Dhruv rang the doorbell.


D: Hey Rhea! Any luck with our cryptic clue yet?


R (frowning): Did you come in here for that?


D (grinning): Just thought I’d come say hi. After all,...


R: Hmm, cut it out! To answer your question, no. Still thinking.


D: I was wondering if we can figure this out, together. I was thinking about this last night. We could begin by trying to understand what the word even means. What is an even number?


R: A number with last digits 0, 2, 4, 6, or 8.


D: Right. But, since Anu ma’am said that we should try and think of it without using the concept of numerals, let’s avoid using this digit-based definition.


R: I really don’t understand what that means. What is the difference between numbers and numerals? Aren’t they the same thing?


D: Hmm, let’s look up ‘numeral’ in the dictionary.


R: Oxford Dictionary gives this meaning of ‘numeral’: “a figure, symbol, or group of figures or symbols denoting a number.” Oh, I think I got...!! (appears suddenly confused). Wait, no! I thought I had figured it out, but I guess not.


D: I think I’m beginning to get it. But I’m unable to describe what I’m thinking. Never mind, let’s have lunch and we’ll ask Anu Ma’am on Monday.


A flash of light and a loud clang! Dhruv looked around him, not remotely surprised, but mildly annoyed. Rhea turned towards the source of the sound and panicked.


R: Oh my god, what is that?


D: Umm, you mean ‘who is that’? That’s Socrates. He keeps showing up. Apparently whenever he feels I’m giving up, he jumps in. I found it really entertaining at first, but sometimes it's a little annoying.


S: Hello Dhruv! It is I, Socrates.


D: Yes, yes, I know! I always know.


S: But you can never be sure!


D (rolls eyes): He always does this.


R: But this is great, Dhruv! Maybe Socrates can help us. Socrates, what’s the difference between numbers and numerals?


S: Rhea, that’s not what I’m here for. I never give away the answers. But I can give you a clue.


R: Alright, a clue then!


S: Let’s look at it this way. How do you write 2 in Hindi?


Rhea drew the symbol on the board: २


S: That’s right. How about Roman 2?


Dhruv drew another symbol on the board: II


S: So, what do 2, २, and II have in common?


R: Umm, they all mean the same thing.


D: And I guess this ‘same thing’ is the ‘number’. Is that what Anu Ma’am was talking about, Socrates?

Socrates? Hellloooo??!


In their excitement, they hadn’t noticed that Socrates was gone!


D (laughing): He always leaves when I get back on track. Ok, now, I’m really hungry!

Pause and Reflect: How does this renewed understanding of numbers and numerals help you understand why Anu ma’am found the proof the class was discussing to be trickery.


Image Credits: Photo by Luca Bravo on Unsplash