A question of fairness

Liri was excited. On her journey through the solar system she had noticed something.

Liri: “Erklärus! Mars has 2 moons. Earth has only one. Is that fair?”
Erklärus: “Fair or not – that’s a question for philosophy. But that 2 is bigger than 1 – that’s a question for mathematics.”
Liri: “And how do you say that in mathematics?”
Erklärus: “With three little signs. The most powerful signs there are – because they can compare anything. Numbers, planets, galaxies.”

He reached for his notebook. Three signs. That was all you needed.

The three comparison signs – click on them!

<
Less than
The left number
is smaller
=
Equal to
Both numbers
are the same size
>
Greater than
The left number
is bigger
← Click on a sign!
Erklärus: “The signs < and > look like a mouth. And the mouth always eats the bigger number!”
Liri: “Like a crocodile?”
Erklärus: “Just like a crocodile. The crocodile is greedy – it always snaps at the bigger one.”

🐊 The crocodile trick

The crocodile always opens its mouth towards the bigger number. Click on the sign to flip it:

3
🐊<
8
The crocodile snaps at the 8 – because 8 is bigger than 3. So: 3 < 8 ✓

Another example – the Plough has 7 stars, the Southern Cross has 4. Which is right?

7
4

Comparisons in the universe – choose the right sign!

Click on the right sign for each comparison:

🪐 Moons of Mars vs. moons of Earth
2
1
🪨 Rocky planets (Mercury, Venus, Earth, Mars) vs. 🌬️ gas planets (Jupiter, Saturn, Uranus, Neptune)
4
4
🌍 Planets smaller than Earth (Mercury, Venus, Mars) vs. planets bigger than Earth (Jupiter, Saturn, Uranus, Neptune)
3
4
🌌 Comparisons in the real universe

Stars in the Plough 7 > stars in the Southern Cross 4
Moons of Mars 2 > moons of Earth 1
Rocky planets 4 = gas planets 4

Without comparison signs, astronomers couldn’t say which constellation has more stars, which planet has more moons, and where there are exactly the same number.

⚖️ Exercise 1 – The right sign
Our solar system has 8 planets and 5 recognised dwarf planets (like Pluto). Which sign belongs in between?
<
>
=
⚖️ Exercise 2 – Crocodile test
The crocodile always snaps at the bigger number. There are 4 rocky planets and 4 gas planets. Where does the crocodile snap in 4 ☐ 4?
<
>
=
⚖️ Exercise 3 – Universe
Liri still has 25 light-years to go to get home. Her friend Alpha still has 9 light-years. Who is further away?
Liri – because 25 > 9
Alpha – because 9 > 25
Both the same distance
❌ Common mistake in thinking

Many people mix up < and >. A simple trick:

The pointed end always points to the smaller number.
3 < 8 → the point faces the 3, because 3 is smaller.
8 > 3 → the point faces the 3, because 3 is smaller.

And when two numbers are exactly the same size, like 4 = 4, you use the equals sign – no crocodile needed!

The end of this night

Liri thought for a long time about the three signs.

Liri: “So: Mars has more moons than Earth. Mars > Earth – at least as far as moons go.”
Erklärus: “Correct. But when it comes to size, Earth wins again – it is bigger than Mars.”
Liri: “And what else does Earth win?”
Erklärus: “Life. As far as we know.”

Liri glowed warm and golden. That was an answer she liked.

Liri: “I remember two star clusters that I passed. One had more stars than the other – but I can’t remember which one.”
Erklärus: “Then we’ll write down both. Sometimes a map needs open questions too.”
“Second lesson: three signs are enough to compare anything. < less than. > greater than. = equal to. The crocodile’s mouth always faces the bigger number. The point always faces the smaller one.”
The three comparison signs
a < b    a = b    a > b
less than  ·  equal to  ·  greater than  ·  The point always faces the smaller number
🌟

Chapter 2 mastered!

Erklärus and Liri can now compare numbers up to 20 – in the classroom and in the universe. The journey goes on.

Erklärus’s notebook – page 2:
“Three signs: < > = . The mouth eats the bigger one. The point faces the smaller one. Mars has 2 moons, Earth only 1: 2 > 1. Rocky planets and gas planets are equal in number: 4 = 4. Liri thinks it’s fair that Earth at least wins when it comes to life. So do I.

Memory map, point 2: two star clusters of different sizes – which one was bigger is still an open question.”
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← Back to overview 2 – Comparison Signs