Class 9 Maths Ch 3 The World of Numbers | One-to-one correspondence: counting without number words

A herder with no word for any number still has to know, before dark, that every animal is back. One pebble out, one pebble in — and it works. Full topic page, with the transcript and the exact book reference: https://prepshorts.com/learn/class-9/... A herder with no word for any number still has to know, before dark, whether every animal is back. He drops one pebble into a pot as each one leaves and takes one out as each one returns, and at dusk the pot answers exactly: empty means all back, two pebbles left means two still out. Nothing is counted and no number is ever spoken - the comparison is performed by the objects. Then the interesting half. Ask him how big the herd is and the pot refuses: two pebbles are left by 23 out with 21 back, by 40 out with 38 back, and by a herd of 2 with none back at all. Scanning every herd up to forty, thirty-nine of them end with two pebbles, and all thirty-nine are different sizes. The method answers one question and refuses the other, which is exactly the difference between knowing none are missing and knowing how many there are. Number names are one way of recording a pairing, not what counting is - and not the only way: four fingers with three joints each give twelve on one hand, which is where grouping by twelve comes from, so ten is a choice with a reason rather than a law. Pebbles get knocked over, so cut the marks into bone. That is the same pairing made permanent, and permanence is what lets a record be compared and rearranged. One bone carries twenty-nine notches, close to the moon's cycle, and is read as either a lunar counter or a menstrual calendar - both add one mark a day over the same span, so the record cannot tell them apart. CHAPTERS 0:00 A herd at dusk 0:51 One pebble for each animal 1:37 One pebble back out 2:15 Reading the pot 3:11 What the pot never tells you 3:55 Twelve on one hand 4:48 Pebbles do not survive the day 5:35 Twenty-nine notches 6:28 Four groups on a bone 7:07 The trap at twenty-one 7:46 A grouped tally is making a claim 8:32 Where the pairing runs out IN THE BOOK Class 9 Mathematics, Chapter 3, "The World of Numbers". NCERT Ganita Manjari, Grade 9 Mathematics, NCF-SE 2023 (Part I), printed pp. 41–67. ABOUT PREPSHORTS One short video per NCERT topic, with the book open beside it. Not worked answers to the exercises — the reason each result has to hold, which is the half that carries into a question you have not seen before. The full library is 708 videos across Classes 6 to 12, about 147 hours in all. 88 are free to watch, one opening every chapter. https://prepshorts.com/?utm_source=yo...