## The Principle of Math Induction is Common Sense

Mathematical induction is not a strange concept, but a common sense concept.  If something is true of the base of a chain, and transfers along the chain at each link, then it applies to every link in the chain.

The principle of mathematical induction is made complicated and confusing by making it about infinite sets, and using an awkward terminology from set theory.

When mathematical induction is expressed in plain words, it turns out to be an ordinary notion that is widely understood.

Thus mathematical induction can be taught in first grade.  Moreover, the Peano Axioms can be taught in first grade.

1. Zero is a unique tick on the number line.
2. Each tick on the number line is immediately followed on the right by a unique tick.
3. Zero is not a tick to the right of another tick.
4. If the ticks to the right of two ticks are equal, then said two ticks are equal.
5. If the zero tick is green and green transfers to the next tick, then all the ticks are green.

Other versions of the Peano Axioms are at the following link.

http://newmathdoneright.com/2012/08/11/principle-of-green-tick-number-line-induction/

1. Zero is a unique tick on the number line.
2. Each tick is followed by a unique tick.
3. Zero does not follow any tick.
4. Each tick, other than zero, follows a unique tick.
5. If the zero tick is green and green transfers to the next tick, then all the ticks are green.

51 words.  277 characters. This is below what first graders are often asked to memorize outside of school.

1. Zero is a unique tick.
2. Each tick is followed by a unique tick.
3. Zero does not follow any tick.
4. Each tick after zero follows a unique tick.
5. If the zero tick is green and green transfers to the next tick, then all the ticks are green.
1. Zero is a unique tick.
2. A unique tick follows each tick.
3. Zero does not follow any tick.
4. After zero, each tick follows a unique tick.
5. If the zero tick is green and green transfers to the next tick, then all the ticks are green.

248 characters.

1. Zero is a tick.
2. A tick follows each tick.
3. Zero does not follow any tick.
4. After zero, each tick follows a unique tick.
5. If tick zero is green and each tick transfers green, then all ticks are green.

216 characters.

1. Zero a tick.
2. A tick after a tick.
3. Zero after no tick.
4.  After zero, each tick after a unique tick.
5. If tick zero be green and green transfers, then all ticks be green.

33 words 188 characters.

1. Zero a tick.
2. A tick after a tick.
3. Zero after no tick.
4. Other than zero, each tick one mom.
5. Zero green, green transfers, then all green.

26 words, 156 characters.

1. Zero a tick.
2. A tick then a tick.
3. Zero after no tick.
4. Each tick one mom, else zero.
5. Zero green, green transfers, then all green.

25 words, 151 characters.

1. Zero a tick.
2. A tick then a tick.
3. Zero after no tick.
4. Not zero, one mom.
5. Zero green, green transfers, all green.

22 words 137 characters.

From Wolfram

1. Zero is a number.

2. If is a number, the successor of is a number.

3. zero is not the successor of a number.

4. Two numbers of which the successors are equal are themselves equal.

5. (induction axiom.) If a set of numbers contains zero and also the successor of every number in , then every number is in .

65 words 327 characters.

http://mathworld.wolfram.com/PeanosAxioms.html

## About New Math Done Right

Author of Pre-Algebra New Math Done Right Peano Axioms. A below college level self study book on the Peano Axioms and proofs of the associative and commutative laws of addition. President of Mathematical Finance Company. Provides economic scenario generators to financial institutions.
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