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Numbers and Numerals: A Weekend Exploration

Part 2. Sunday

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